A privately owned summer camp for youngsters has the following data for a 12-wee

Question

A privately owned summer camp for youngsters has the following data for a 12-week session:

Charge per camper $480 per week

Fixed costs   $192,000 per session

Variable cost per camper $320 per week

Capacity 200 campers.

a) Develop the mathematical relationships for total cost and total revenue.

b) What is the total number of campers that will allow the camp to just break even?

c) What is the profit or loss for the 12-week session if the camp operates at 80% capacity?

d) What are marginal and average costs per camper at 80% capacity?

Explanation / Answer

a) Total Cost = $192,000 +( $320 * 12 X) = $192,000 + $3,840 X

    Total Revenue = $480 * 12 x = $5,760 X

b) Breakeven occurs when: Total Cost = Total Revenue$192,000 + $3,840 X = $5,760 X

                                                              1,920 X = $192,000X = 100

c) 80% capacity means

                         X = 80% * 200 = 160 campers

Total Profit (160) = Total Revenue (160) – Total Cost (160)

                              = ($5,760 * 160) – ($192,000 + $3,840 * 160)

                              = $115,200.

d) Average costs = Total cost/total campers = 806400/160 = $5040per camper

Marginal costs = Variable cost = $320*12weeks

                                                  = $3840per camper

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