WBSCTE Diploma Solved Archive · July 2023 · Code: 633/1(N)

July 2023 Solutions

Engineering Economics & Project Management (OE301)

Compulsory Questions Solved MC-AVC Calculus Proofs PPC Slope Analysis NPV 10% Hurdle Solver Horizontal Summation SVGs

Paper Structure & Navigation

  1. Q1: Compulsory Short Answer Questions (a to g)
  2. Q2: Price Elasticity Definitions & Calculus Solvers
  3. Q3: Market Demand Summation & Equilibrium Stability
  4. Q4: Unified Cost Curve Geometries & MC-AVC Calculus Proof
  5. Q5: Profit Maximization Calculus & Structural Market Features
  6. Q6: Project Financial Feasibility & NPV Appraisal
  7. Q7: Detailed Project Life Cycle (PLC) Resource Curve
  8. Q8: Project Management & Financial Ratio Importance
Section 01

Question 1: Short Answer Compulsory Solutions (Answer any 5)

Under WBSCTE guidelines, answers in this section must be academically precise, using clear mathematical and conceptual proofs. They are refactored below into logical systems-engineering frameworks.

Question 1(a)

Explain, in brief, the two basic problems in economics.

Ans: The core economic problem is **scarcity**, which is a **system resource constraint**. Since our raw input vectors (materials, energy, capital, time) are strictly limited while the system requirements (human wants) are infinite, we are forced to make optimization choices. This leads to two basic problems:

1. The Resource Allocation Problem (What and How to Produce): Designing our system. We must decide which outputs to produce with our limited input resources (e.g., consumer goods vs. capital equipment) and which processing technology to use (e.g., labor-intensive manual methods vs. capital-intensive automation) to maximize overall system efficiency.

2. The Distribution Problem (For Whom to Produce): Priority routing. We must decide how to distribute the output among consumers based on purchasing power and income levels, determining which nodes in our network receive the finished products.

Question 1(b)

Define Production Possibility Curve. Why is the curve negatively sloped?

Ans: The **Production Possibility Curve (PPC)** (or Production Possibility Frontier) represents the **Pareto Efficiency Frontier** or maximum capacity boundary of a system. It shows all maximum possible output combinations of two goods (e.g., Good X and Good Y) that an economy can produce using a fixed set of resources and a constant state of technology, assuming the system is running at 100% efficiency.

Why the PPC has a Negative Slope: The PPC slopes downward from left to right because of the **Conservation of Resources**. When the system is operating at full capacity (on the curve), resources are fully utilized. To increase the output of Good X, resources must be diverted away from producing Good Y, causing Y's output to decrease. This trade-off is represented by a negative first derivative: $$\text{Slope of PPC} = \text{Marginal Rate of Transformation (MRT)}_{xy} = -\frac{\Delta Y}{\Delta X} < 0$$

Sacrifice Y (Slope < 0) Good X Good Y O

Question 1(c)

Distinguish between change in demand and change in quantity demanded.

Ans: In systems analysis, this is the difference between shifting the operating point of a system and re-biasing the system's baseline characteristics:

Basis of Comparison Change in Quantity Demanded (Operating Point Shift) Change in Demand (System Re-Biasing)
Primary Cause Exclusively a change in the own price of the commodity ($P_x$). This price acts as the primary input control signal. Changes in **non-price parameters** (e.g., consumer income budget, user preferences, price of parallel substitutes).
Geometry Sliding the operating point along the **same** stationary demand curve. The **entire** demand curve physically shifts leftward or rightward to a new position.
Terminology Expansion (downward-right movement) or Contraction (upward-left movement). Increase in Demand (rightward shift) or Decrease in Demand (leftward shift).

Question 1(d)

A cost curve is given by $C = a + bq + dq^2$; where $q$ stands for quantity. Find Fixed cost, Variable cost, and Average Variable cost.

Ans: Given the short-run total cost function: $C(q) = a + bq + dq^2$.

1. Total Fixed Cost (TFC - Static Offset / Idle Power): Fixed costs are independent of the system's output level ($q$). We find this static offset by setting $q=0$: $$\text{TFC} = C(0) = a$$ 2. Total Variable Cost (TVC - Dynamic Operating Impedance): The part of the cost function that scales with throughput ($q$). We find this by subtracting the fixed cost from total cost: $$\text{TVC} = C(q) - \text{TFC} = (a + bq + dq^2) - a = bq + dq^2$$ 3. Average Variable Cost (AVC - Specific Dynamic Loss): The variable cost per unit of output: $$\text{AVC} = \frac{\text{TVC}}{q} = \frac{bq + dq^2}{q} = b + dq$$

Question 1(e)

State any three objectives of a project.

Ans: In project management, these are the three constraints of the **triple constraint triangle**:
1. Time Bound (Latency): Completing the project's work on or before its scheduled deadline.
2. Cost Bound (Resource Envelope): Completing all work within the approved budget limit.
3. Scope and Quality Compliance: Meeting all performance, technical, and quality requirements.

Question 1(f)

Discuss in brief, some of the adverse impacts of a project on environment.

Ans: Large infrastructure, civil, or industrial projects can have significant environmental impacts (negative system externalities):
• Pollution (Off-Gassing): Releasing toxic pollutants into air, water, and soil during construction and operation.
• Ecosystem Disruption: Clearing forests, destroying natural habitats, and displacing local wildlife.
• Resource Drain: High consumption of fresh water, energy, and non-renewable raw materials.

Question 1(g)

Discuss the differences (any three) between PERT and CPM.

Ans: PERT and CPM use different scheduling logic to manage projects:

Feature PERT (Program Evaluation & Review Technique) CPM (Critical Path Method)
Nature of Durations Probabilistic: Activity durations are uncertain and estimated using three timeframes ($t_o, t_m, t_p$). Deterministic: Activity durations are known with reasonable certainty based on historical data.
Focus Event-oriented: Designed to monitor and control major milestones. Activity-oriented: Designed to optimize and control task durations.
Best Suited For Non-repetitive, high-uncertainty projects (such as R&D). Repetitive, predictable projects (such as construction).
Section 02

Question 2: Price Elasticity of Demand & Calculus Solvers

Question 2: (i) Define Price Elasticity of Demand. (ii) What is the unit of price elasticity of demand? (iii) Suppose the demand function for a product is given by: $q = 500 - 10p$. (a) Compute the price elasticity of demand when the price of the product is Rs. 30 per unit. (b) State whether the product is necessary or luxury.

Answer 2(i): Price Elasticity Definition

Price Elasticity of Demand ($E_p$): Measures the responsiveness of the quantity demanded of a commodity to changes in its own price, holding other factors constant. In engineering, this is the **sensitivity / gain** of the demand system. It is calculated as: $$E_p = -\left( \frac{\%\text{ Change in Quantity Demanded}}{\%\text{ Change in Price}} \right) = -\left( \frac{\Delta q}{\Delta p} \times \frac{p}{q} \right)$$ Using calculus, the point elasticity formula is: $$E_p = -\left( \frac{dq}{dp} \times \frac{p}{q} \right)$$

Answer 2(ii): Unit of Price Elasticity

The price elasticity of demand is a **pure number** and has **no unit of measurement** (it is dimensionless). Since it is calculated as a ratio of percentage changes, any units of price and quantity cancel out, allowing economists to compare elasticity across different goods and currencies.

Answer 2(iii): Numerical Elasticity Calculation

Given the demand function: $$q = 500 - 10p$$ Step 1: Differentiate quantity with respect to price to find the marginal change
$$\frac{dq}{dp} = \frac{d(500 - 10p)}{dp} = -10$$ Step 2: Find quantity ($q$) at the target price $p = 30$ Rs.
$$q = 500 - 10(30) = 500 - 300 = 200 \text{ units}$$ Step 3: Calculate the point price elasticity of demand ($E_p$)
$$E_p = -\left( \frac{dq}{dp} \times \frac{p}{q} \right)$$ $$E_p = -\left( -10 \times \frac{30}{200} \right) = \frac{300}{200} = 1.5$$ Step 4: Assess luxury vs. necessity classification
- If $E_p < 1$, the good is inelastic, typically representing a necessity (buyers continue purchasing even as prices rise).
- If $E_p > 1$, the good is elastic, typically representing a luxury (buyers are highly responsive to price changes).

Since the calculated elasticity is **$E_p = 1.5$ (which is greater than $1$)**, demand is relatively elastic, indicating that the product is a luxury good.
Section 03

Question 3: Market Demand Derivation & Equilibrium Stability

Question 3: (i) How will you derive market demand curve from individual demand curves? (ii) What do you mean by market equilibrium? (iii) When is market equilibrium stable? (iv) Let the market demand function be $q = 10 - 0.4p$ and the market supply function be $q = 5 + 0.6p$. Find the equilibrium price and quantity.

Answer 3(i): Horizontal Summation of Individual Demands

The market demand curve represents the total quantity of a good demanded by all buyers in the market at each price level. It is derived through the **horizontal summation of all individual demand curves**.

Systems Process: In parallel circuits, we sum individual branch currents to find the total current. Similarly, at each price level, we sum the quantities demanded by each individual buyer. Repeating this at every price level yields the market demand curve, which is flatter than individual demand curves.

Figure 2 — Horizontal Summation of Demand Curves

Consumer 1 (d1) + Consumer 2 (d2) = Market Demand (D = d1 + d2) P q1 q2 Q = q1+q2

Answer 3(ii): What is Market Equilibrium?

Market Equilibrium is a state of balance where the quantity of a product demanded by buyers exactly equals the quantity supplied by sellers at the prevailing price. In engineering terms, this is a **stable zero-error state** where the rate of source supply matches the sink demand. At this price point, known as the **market-clearing price**, there are no market surpluses or shortages.

Answer 3(iii): Stability of Market Equilibrium

A market equilibrium is **stable** if any deviation from the equilibrium price triggers automatic feedback loops that push the price back toward the equilibrium level.

Stability Condition: An equilibrium is stable when the demand curve is downward-sloping and the supply curve is upward-sloping. Under these conditions:

Answer 3(iv): Equilibrium Price-Quantity Calculation

Given functions: $$q = 10 - 0.4p \quad \text{(Demand)} \quad \text{and} \quad q = 5 + 0.6p \quad \text{(Supply)}$$ Setting quantity demanded equal to quantity supplied ($q_d = q_s$): $$10 - 0.4p = 5 + 0.6p$$ Group like terms: $$10 - 5 = 0.6p + 0.4p \implies 5 = 1.0p$$ $$p^* = 5 \text{ Rs.}$$ Substitute $p^* = 5$ back into either equation to find $q^*$: $$q^* = 10 - 0.4(5) = 10 - 2 = 8 \text{ units}$$ Verify using the supply function: $$q^* = 5 + 0.6(5) = 5 + 3 = 8 \text{ units}$$ Final Answer: The market-clearing equilibrium price is $p^* = \text{Rs. } 5$, and the equilibrium quantity is $q^* = 8\text{ units}$.
Section 04

Question 4: Unified Cost Curve Geometries & MC-AVC Proof

Question 4: (i) Draw a single diagram to show the shapes of Average Fixed cost, Average Variable cost, Average Total cost and Marginal cost. (ii) Show that the Marginal cost passes through the minimum point of Average Variable cost.

Answer 4(i): Unified Cost Curves Diagram

Figure 3 — Short-Run Average and Marginal Cost Curves

AFC AVC ATC MC Min AVC Min ATC Quantity (q) Price / Cost O

Note two key geometric relationships: (1) The vertical distance between ATC and AVC declines continually because AFC falls but never equals zero, (2) The **MC curve cuts both AVC and ATC from below at their lowest points**.

Answer 4(ii): Mathematical Proof of MC-AVC Intersection

Calculus-Based Proof:
Let Total Variable Cost be $TVC(q)$ and quantity be $q$. By definition, Average Variable Cost ($AVC$) is: $$AVC = \frac{TVC}{q} \implies TVC = AVC \cdot q$$ To find the output level where $AVC$ is minimized, we take the derivative of $AVC$ with respect to output $q$ and set it to zero ($\frac{d(AVC)}{dq} = 0$): $$\frac{d(AVC)}{dq} = \frac{d}{dq} \left( \frac{TVC}{q} \right) = 0$$ Using the quotient rule of differentiation: $$\frac{q \cdot \frac{d(TVC)}{dq} - TVC \cdot \frac{dq}{dq}}{q^2} = 0$$ Since $q > 0$ at any positive output level, the numerator must equal zero: $$q \cdot \frac{d(TVC)}{dq} - TVC = 0$$ By definition, the derivative of total variable cost with respect to quantity is **Marginal Cost** ($MC = \frac{d(TVC)}{dq}$). Substituting this in: $$q \cdot MC - TVC = 0 \implies q \cdot MC = TVC$$ Divide both sides by $q$: $$MC = \frac{TVC}{q}$$ Since $\frac{TVC}{q}$ is the definition of $AVC$, we have: $$MC = AVC$$ Conclusion: This proof shows that at the minimum point of $AVC$, **Marginal Cost must equal Average Variable Cost** ($MC = AVC$), meaning the MC curve intersects the AVC curve exactly at its minimum point.
Section 05

Question 5: Profit Maximization & Market Structure

Question 5: (i) If the demand is given by $p = 80 - 3q$ and Total Cost is $C = 12 + 2q^2$, then write the profit function. Calculate profit maximizing price and profit maximizing quantity. (ii) Compare the features of a perfectly competitive market and a monopoly market.

Answer 5(i): Calculus Profit Maximization

Given functions: $$\text{Demand: } p = 80 - 3q \quad \text{and} \quad \text{Total Cost: } C = 12 + 2q^2$$ Step 1: Write the Total Revenue ($TR$) function
$$TR = p \cdot q = (80 - 3q)q = 80q - 3q^2$$ Step 2: Write the Profit Function ($\Pi$)
$$\Pi(q) = TR - TC$$ $$\Pi(q) = (80q - 3q^2) - (12 + 2q^2) = -5q^2 + 80q - 12$$ Step 3: Apply the First-Order Condition (FOC) for profit maximization
Take the derivative of the profit function with respect to $q$ and set it to zero ($\frac{d\Pi}{dq} = 0$): $$\frac{d\Pi}{dq} = \frac{d(-5q^2 + 80q - 12)}{dq} = -10q + 80 = 0$$ $$10q = 80 \implies q^* = 8 \text{ units}$$ Step 4: Verify the Second-Order Condition (SOC)
The second derivative of the profit function must be negative to confirm a stable peak: $$\frac{d^2\Pi}{dq^2} = \frac{d(-10q + 80)}{dq} = -10 < 0 \quad (\text{Sufficient Condition Met!})$$ Step 5: Calculate the profit-maximizing price ($p^*$)
Substitute the optimal quantity $q^* = 8$ back into the demand function: $$p^* = 80 - 3(8) = 80 - 24 = 56 \text{ Rs.}$$ Step 6: Compute the resulting maximum profit ($\Pi^*$)
$$\Pi^* = -5(8)^2 + 80(8) - 12 = -320 + 640 - 12 = 308 \text{ Rs.}$$ Final Answer: The profit-maximizing quantity is $q^* = 8\text{ units}$, the profit-maximizing price is $p^* = \text{Rs. } 56$, and the maximum economic profit is **Rs. 308**.

Answer 5(ii): Market Structure Comparison

Feature Perfect Competition (Zero-Impedance Node) Monopoly (Unidirectional Driver)
Seller Concentration An infinite number of small, independent sellers. A single seller controls the entire market supply.
Product Nature Homogeneous products (goods are perfect substitutes). Unique product with no close substitutes available.
Market Power Firm is a Price Taker (no market control). Firm is a Price Maker (complete market control).
Demand Curve Perfectly horizontal, infinitely elastic curve ($E_p = \infty$). Downward-sloping demand curve ($E_p < \infty$).
Long-run Profit Firms can only earn **normal profits** in the long run. The monopolist can earn **supernormal profits** in the long run.
Revenue Linkage $\text{Price} = AR = MR$ $AR > MR$
Section 06

Question 6: Financial Feasibility & NPV Appraisal

Question 6: (i) State any two methods of evaluating the financial feasibility of a project. (ii) State one advantage and one disadvantage of using payback period. (iii) Suppose the initial cost of a project is Rs. 40,000 and is expected to generate the following returns in the next 4 years: 16,000, 14,000, 12,000, 10,000. If the market rate of interest is 10% then calculate the NPV of the project and state whether the project will be undertaken or not?

Answer 6(i): Financial Feasibility Methods

  1. Net Present Value (NPV) Method: A discounted cash flow method that discounts all expected cash flows back to the present using the required rate of return.
  2. Payback Period Method: A non-discounted method that calculates the time required to recover the initial investment from net cash inflows.

Answer 6(ii): Payback Period Pros & Cons

Answer 6(iii): Detailed NPV Calculation

To analyze the project, we treat future cash inflows as **attenuated signals** ($CF \cdot (1+r)^{-t}$) passing through a lossy transmission line over time, discounting them back to the present:

Given Financial Parameters:
- Initial Investment Outlay ($CF_0$) = Rs. $40,000$
- Required Discount Rate ($r$) = $10\% \implies (1.1)^{-t}$ discount factors
- Project Lifespan = $4$ Years
- Inflows ($CF_t$): $Y_1 = 16,000$; $Y_2 = 14,000$; $Y_3 = 12,000$; $Y_4 = 10,000$
Year ($t$) Inflow ($CF_t$ in Rs.) Discount Factor at 10% ($\frac{1}{(1.1)^t}$) Present Value ($PV_t$ in Rs.)
1 16,000 $0.9091$ $16,000 \times 0.9091 = 14,545.60$
2 14,000 $0.8264$ $14,000 \times 0.8264 = 11,569.60$
3 12,000 $0.7513$ $12,000 \times 0.7513 = 9,015.60$
4 10,000 $0.6830$ $10,000 \times 0.6830 = 6,830.00$
Total Present Value of Inflows (PVCI): Rs. 41,960.80
Calculate Net Present Value (NPV): $$\text{NPV} = \text{PVCI} - CF_0$$ $$\text{NPV} = 41,960.80 - 40,000 = +1,960.80 \text{ Rs.}$$ Financial Decision Verdict:
Since the Net Present Value is positive (**$\text{NPV} = +1,960.80 \text{ Rs.} \ge 0$**), the project will recover its initial costs and meet the required 10% rate of return. Therefore, the project is financially viable and should be undertaken.
Section 07

Question 7: The Project Life Cycle (PLC)

Question 7: Discuss the Life Cycle of a project. (9 Marks)

Detailed Analysis of the Four PLC Phases (Transient Operating States)

To secure full marks on a 9-mark essay, we model the project's life cycle as four consecutive states of a transient run:

  1. 1. Conceptualization and Initiation Phase (Initial Impedance Check): The system's requirements and objectives are identified. Key activities include:
    • Defining project scope, objectives, and deliverables.
    • Conducting preliminary market and economic feasibility studies.
    • Identifying key stakeholders and getting the project charter approved.
  2. 2. Project Formulation and Planning Phase (System Configuration): A detailed project plan is created to guide execution. Key activities include:
    • Developing a detailed Work Breakdown Structure (WBS).
    • Scheduling networks and dependencies (using Gantt charts and PERT/CPM diagrams).
    • Estimating resource costs and defining risk mitigation plans.
  3. 3. Implementation and Execution Phase (Peak Resource Loading / Current Draw): The active execution phase. Hardware and resources are deployed, systems are built and integrated, and the physical assets are constructed. Key activities include:
    • Procuring raw materials and equipment.
    • Performing physical construction, software coding, or engineering assembly.
    • Tracking budget and schedule variances and managing changes.
  4. 4. Project Completion and Termination Phase (Decommissioning & Post-Audit): The final operational state. Activities include system integration testing, handing over the deliverables to the client, releasing project resources, and conducting post-project performance audits.

Project Life Cycle Resource Loading Curve

Figure 4 — PLC Effort Level Over Time

1. Conception 2. Planning 3. Execution 4. Closeout Peak Effort Stage Time Resource Cost O
Question 08

Question 8: Project Management & Financial Ratio Importance

Question 8: (i) Discuss the importance of Project Management. (ii) What is the importance of calculating financial ratios of a project?

Answer 8(i): Importance of Project Management

Project management provides the tools, techniques, and methodologies needed to successfully deliver projects on time, within budget, and to specifications. Its primary benefits include:

Answer 8(ii): Importance of Financial Ratios in Projects (Diagnostic Solvency Monitors)

Financial ratios are critical tools for evaluating a project's financial health, feasibility, and risk profile. They act as **system performance monitors** or diagnostics:

  1. 1. Assessing Short-Term Liquidity (System Charge Buffers): Ratios like the Current Ratio and Quick Ratio help verify that a project has enough liquid assets (charge buffer) to pay its short-term debts and operating expenses on time.
  2. 2. Evaluating Structural Solvency (Leverage Impedance): Ratios like the Debt-Equity Ratio help investors assess a project's capital structure and long-term financial risk, indicating its reliance on debt financing compared to equity.
  3. 3. Measuring Commercial Profitability (Operating Gain Factors): Ratios like Net Profit Margin and Return on Investment (ROI) evaluate how efficiently a project generates earnings relative to its sales or invested capital.
  4. 4. Benchmarking Performance: Financial ratios allow managers to compare a project's financial performance against industry standards or competing investment opportunities.
Critical Review

Key Exam Points to Memorize

Core principles matching past-year questions:

Curve Geometries

  • AFC → Rectangular Hyperbola
  • TFC → Perfectly Horizontal Line
  • MC, AVC, ATC → Classic U-shaped
  • TVC, TC → Inverse S-shaped

Equilibrium Relations

  • MC = MR cuts from below (Profit Max)
  • MC cuts AC & AVC at their minimums
  • At Q=0, TC = TFC (since TVC=0)
  • TC − TVC = TFC (Parallel Curves)

Decision Criteria

  • Accept Project if NPV ≥ 0
  • Reject Project if NPV < 0
  • Critical path tasks have zero float
  • PERT expects probabilistic durations
Past-Paper & Model Questions

Solved PYQ Practice Questions

Project Concept — 5 Marks

Q: Define a Project. What are its core characteristics?

Ans: A project is a temporary endeavor undertaken to produce a unique product, service, or result. Its core characteristics include:
1. **Temporary:** It has a defined beginning and a definite end date.
2. **Unique:** The final deliverable is distinct from regular business operations.
3. **Progressive Elaboration:** The project is planned and executed in detailed, incremental stages.
4. **Constraints:** It must operate within fixed cost, resource, scope, and schedule boundaries.

Network Theory — 5 Marks

Q: Distinguish between PERT and CPM network scheduling techniques.

Ans: - **PERT** is probabilistic. It uses three time estimates ($t_o, t_m, t_p$) to calculate expected activity durations, making it ideal for non-repetitive projects with high uncertainty, like R&D.
- **CPM** is deterministic. It assumes activity durations are known with reasonable certainty, making it ideal for predictable, repetitive construction or maintenance projects.

Financial Risk — 8 Marks

Q: How can environmental, social, and political issues throw an engineering project into uncertainty?

Ans: Engineering projects exist within dynamic social and regulatory systems:
1. **Environmental clearance delays:** Protests or environmental impact assessments can delay projects for years, driving up costs.
2. **Socio-political protests:** Local communities may protest land acquisition, cultural heritage issues, or potential pollution, causing work stoppages.
3. **Regulatory shifts:** Sudden changes in safety standards, carbon taxes, or government policies can force costly project redesigns or contract cancellations.

Short Notes — 5 Marks

Q: Write short notes on Working Capital and Debt-Equity Ratio.

Ans: - **Working Capital:** The capital used to fund a business's day-to-day operations, calculated as Current Assets minus Current Liabilities. It excludes long-term capital assets like land.
- **Debt-Equity Ratio:** A solvency ratio that compares long-term debt to shareholders' equity, measuring financial leverage. A ratio of **2:1** is the standard benchmark in capital-intensive industries.

Revision Sheets

Ultra-Condensed Revision Panels

Life Cycle Stages

  • Initiation: Conceptualization, feasibility
  • Planning: Detail schedules, budget
  • Execution: Physical work begins
  • Closeout: Client handover, post-audit
  • Post-audit: Termination phase

PERT Calculations

  • Expected: $t_e = \frac{t_o + 4t_m + t_p}{6}$
  • Variance: $\sigma^2 = \left( \frac{t_p - t_o}{6} \right)^2$
  • Normal Distribution models path probability
  • Used for uncertain, unique R&D

CPM Network

  • Forward Pass: Calculates $ES$ and $EF$
  • Backward Pass: Calculates $LS$ and $LF$
  • Critical Path: Longest path ($Float = 0$)
  • Total Float: $LS - ES$ or $LF - EF$

Capital Budgeting

  • Payback: ignores time value & tail cash
  • $\text{NPV} = \sum \frac{CF_t}{(1+r)^t} - CF_0$
  • Accept if NPV ≥ 0
  • Sensitivity: highly sensitive to discount rates

July 2023 Economics & Project Management Solutions · Compiled for academic excellence.