Question

The cost of running a movie theatre is Rs. 10,000 per day, plus additional Rs. 5000 per show. The theatre has 200 seats. A new movie released on Friday. There were three shows, where the ticket price was Rs. 250 each for the first two shows and Rs. 200 for the late-night show. For all shows together, total occupancy was 80\%. What was the maximum amount of profit possible ?

• A. Rs. 1,20,000
• B. Rs. 1,16,000
• C. Rs. 91,000
• D. Rs. 95,000
• E. Rs. 87,500

Hint:

In maximization problems involving mixed pricing and a fixed total capacity, always allocate the highest volume to the highest-priced tier first to maximize overall revenue.

Answer 1

The Correct Option is C

Step 1: Calculate the total cost.
Total fixed cost = Rs. 10,000.
Cost for 3 shows = $3 \times 5,000 =$ Rs. 15,000.
Total Cost = $10,000 + 15,000 =$ Rs. 25,000.

Step 2: Determine maximum possible revenue.
Total seats available across 3 shows = $3 \times 200 = 600$ seats.
Given 80% occupancy, total tickets sold = $0.80 \times 600 = 480$ tickets.
To maximize profit, we must maximize revenue by selling as many high-priced tickets as possible.
Maximum seats for the first two shows (Rs. 250 tickets) = 400 seats.
Remaining tickets to be sold for the late-night show (Rs. 200 tickets) = $480 - 400 = 80$ tickets.

Step 3: Calculate maximum profit.
Maximum Revenue = $(400 \times 250) + (80 \times 200) = 100,000 + 16,000 =$ Rs. 116,000.
Maximum Profit = Revenue - Cost = $116,000 - 25,000 =$ Rs. 91,000.