Problem $2[35$ pts$][$Textbook Problem $2-15$ Based$]$

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?