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?

a) (480-320) X - 192,000

where:

X is the camper amount which is an integer between;

0 < X <200

b) it will require 1,200 over the course of 12 weeks

c) operating gain of 115,200

d) marginal cost at 80% capacity: 320

average cost: 420 per camper per week

Explanation:

b) contribution per camper:

480 - 320 = 160 dollars

fixed cost 192,000

192,000 / 160 = 1,200 campers

c) at 80% capacity:

200 camper x 12 weeks x 80% x 160 contribution =

307.200‬ contribution

- 192,000 fixed cost

115,200 operating gain

d) the marginal cost per camper would be the 320 cost per week as the fixed cost are incurrent already thus, each new camper cost is only their variable cost.

the average cost per camper will be:

200 camper x 12 weeks x 80% = 1,920 campers

the average cost would be the sum of variable and fixed cost:

(1,920 x 320 + 192,000) / 1,920 = 420‬

we cna verify this:

(480 - 420) x 1,920 = 115.200‬

we get the same income as before thus, the calculation are correct.