A laptop company's annual sales depend on the market states and whether a brand ambassador is used for advertising. The market consists of three states: State I, State II, and State III with probabilities 0.4, 0.4, and 0.3 respectively. The selling price per laptop is Rs. 40,000 and the cost price is Rs. 38,500. The targeted annual sales (in units) are given below:

| Market State | With Brand Ambassador | Without Brand Ambassador |
|--------------|-----------------------|--------------------------|
| State I | 10,000 | 8,000 |
| State II | 8,000 | 5,000 |
| State III | 5,000 | 3,000 |

If the company signs a contract with Mr. X for Rs. 24.5 lakh, the cost price of each laptop increases by Rs. 100 in all market states. Assuming the selling price remains unchanged, what is the total profit earned by the company after paying Mr. X?

Use the formula for expected profit: $$ ext{Expected Profit} = \sum X_i P_i$$ where $X_i$ is the profit in each market state and $P_i$ is the probability of that state.

Question

A laptop company's annual sales depend on the market states and whether a brand ambassador is used for advertising. The market consists of three states: State I, State II, and State III with probabilities 0.4, 0.4, and 0.3 respectively. The selling price per laptop is Rs. 40,000 and the cost price is Rs. 38,500. The targeted annual sales (in units) are given below:

| Market State | With Brand Ambassador | Without Brand Ambassador |
|--------------|-----------------------|--------------------------|
| State I      | 10,000                | 8,000                    |
| State II     | 8,000                 | 5,000                    |
| State III    | 5,000                 | 3,000                    |

If the company signs a contract with Mr. X for Rs. 24.5 lakh, the cost price of each laptop increases by Rs. 100 in all market states. Assuming the selling price remains unchanged, what is the total profit earned by the company after paying Mr. X?

Use the formula for expected profit: $$	ext{Expected Profit} = \sum X_i P_i$$ where $X_i$ is the profit in each market state and $P_i$ is the probability of that state.

Accepted Answer

**Solution:**

1. **Calculate profit per unit with brand ambassador after contract:**
   - Original cost price = Rs. 38,500
   - Increase in cost price due to contract = Rs. 100
   - New cost price = 38,500 + 100 = Rs. 38,600
   - Selling price = Rs. 40,000
   - Profit per unit = 40,000 - 38,600 = Rs. 1,400

2. **Calculate expected sales units with brand ambassador:**
   - State I: 10,000 units with probability 0.4
   - State II: 8,000 units with probability 0.4
   - State III: 5,000 units with probability 0.3

3. **Calculate expected units sold:**
   $$10,000 	imes 0.4 + 8,000 	imes 0.4 + 5,000 	imes 0.3 = 4,000 + 3,200 + 1,500 = 8,700$$ units

4. **Calculate expected profit with brand ambassador:**
   $$1,400 	imes 8,700 = 12,180,000 = Rs. 121.8 	ext{ lakhs}$$

5. **Calculate expected profit without brand ambassador:**
   - Profit per unit without brand ambassador = 40,000 - 38,500 = Rs. 1,500
   - Expected sales units without brand ambassador:
     $$8,000 	imes 0.4 + 5,000 	imes 0.4 + 3,000 	imes 0.3 = 3,200 + 2,000 + 900 = 6,100$$ units
   - Expected profit without brand ambassador:
     $$1,500 	imes 6,100 = 9,150,000 = Rs. 91.5 	ext{ lakhs}$$

6. **Calculate net profit after paying Mr. X:**
   $$	ext{Net profit} = 121.8 - 91.5 - 24.5 = 5.8 	ext{ lakhs}$$

**Answer:** Rs. 5.8 lakhs

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