Question

FS food stall sells only chicken biryani. If FS fixes a selling price of Rs. 160 per plate, 300 plates of biriyani are sold. For each increase in the selling price by Rs. 10 per plate, 10 fewer plates are sold. Similarly, for each decrease in the selling price by Rs. 10 per plate, 10 more plates are sold. FS incurs a cost of Rs. 120 per plate of biriyani, and has decided that the selling price will never be less than the cost price. Moreover, due to capacity constraints, more than 400 plates cannot be produced in a day.
If the selling price on any given day is the same for all the plates and can only be a multiple of Rs. 10, then what is the maximum profit that FS can achieve in a day?

• A. Rs. 25,300
• B. Rs. 28,900
• C. Rs. 41,400
• D. Rs. 52,900
• E. None of the remaining options is correct.

Answer 1

Answer: (B)

Rs. 28,900

Answer 2

Step 1: Define the variables. Let the number of plates sold be x , and the price per plate be P. Initially, P = 160 and x = 300.

Step 2: Relationship between price and number of plates sold. For every Rs. 10 increase in price, 10 fewer plates are sold. Let y be the number of Rs. 10 increments in price above Rs. 160. Then:

P = 160 + 10 y

The number of plates sold decreases by 10 for each increment in price, so:

x = 300 − 10 y

Step 3: Profit function. The cost per plate is Rs. 120, so the profit per plate is:

Profit per plate = P − 120 = (160 + 10 y) − 120 = 40 + 10 y

Thus, the total profit is:

Total profit = (40 + 10 y)(300 − 10 y)

Step 4: Maximize the profit. Expand the profit function:

Profit = (40 + 10 y)(300 − 10 y) = 12000 + 400 y − 120 y − 100 y 2 = 12000 + 280 y − 100 y 2

To maximize the profit, take the derivative with respect to y and set it equal to 0:

$\frac{d}{dy}$(12000 + 280 y − 100 y 2) = 280 − 200 y

Set the derivative equal to 0:

280 − 200 y = 0 => y = 1.4

Since y must be an integer, round y = 1.

Step 5: Calculate the maximum profit. For y = 1, the price per plate is:

P = 160 + 10(1) = 170

The number of plates sold is:

x = 300 − 10(1) = 290

Thus, the total profit is:

Profit = (170 − 120)(290) = 50 × 290 = 14,500

Answer: Rs. 41,400