Question

1. A privately-owned summer camp for kids has the following revenue and cost data for a 6-week camp session:
   • Charge per camper (i.e., revenue): $120/week
   • Fixed costs per session: $15,000
   • Variable cost per camper: $80/week
   • Capacity: 200 campers

Given this data and assuming campers stay for the whole session, answer the following:

1. Develop and graph the mathematical relationships for total cost and total revenue as a function of the number of campers attending.
2. What is the total number of campers that would allow the camp to just break even?
3. What is the profit or loss for the 6-week session if the camp operates at 80% capacity?
4. What are the average and marginal costs per camper at 80% capacity?

Answer 1

Charge per camper = $120/week

Charge per camper for 6 weeks(REVENUE) = 120*6 = $ 720

Fixed Cost = $15000

Variable cost per week = $80

Variable cost for 6 weeks = 80*6 = $480

Let Total Number of Campers attending be Q.

Ans a)

Total Cost = Fixed Cost + Variable cost per camper for 6 weeks * Total number of campers attending

Total Cost = 15000 + 480*Q

Total Revenue = Charge per camper for 6 weeks * Total number of campers attending

= 720*Q

GRAPH

Ans b)

For break-even

REVENUE = Cost

Therefore for the camp to be break-even there must be at least 63 Campers. We take the upper limit in case of a non-integral value.

Ans c)

Operating at an 80% Capacity would mean that there will 80% of 200 campers, that is, only 160 campers.

Total revenue = 720* 160 = $115200

Total Cost = 15000 + 480*160 = $91800

Cost < Revenue, hence it is a profit

Profit = Revenue - Cost

= 115200 - 91800

= $23400

Total Profit at 80% Capacity = $23400

Ans d)

Average Cost per camper at 80% capacity = Total cost at 80% Capacity / (160)

= 91800 / 160

= $573.75

Average Cost per camper at 80% capacity = $573.75

the marginal cost per camper at 80% Capacity = Cost of 161 Campers - Cost of 160 campers

= 92280 - 91800

= $ 480

the marginal cost per camper at 80% Capacity = $480

This marginal cost indicates the cost of having JUST 1 MORE camper. and is calculated equal to the 480 which is the multiple of Q in the total cost Function ( 15000 + 480*Q).