Question

Tippalee Ventures Inc. provides helicopter tours of the wilderness. The fixed monthly cost for the helicopter, gear, and airport space is $42,500. The variable cost per tour is $6,500. The helicopter tours sell for $3,500 per person, and the helicopter seats three customers. Assuming every helicopter is filled to capacity, what is the break-even volume for the company? What is the break-even volume if each helicopter only carries two customers?

Answer 1

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Question #57110, Economics / Microeconomics

Tippalee Ventures Inc. provides helicopter tours of the wilderness. The fixed monthly cost for the helicopter, gear, and airport space is $42,500. The variable cost per tour is $6,500. The helicopter tours sell for $3,500 per person, and the helicopter seats three customers.

a) Assuming every helicopter is filled to capacity, what is the break-even volume for the company?

b) What is the break-even volume if each helicopter only carries two customers?

Solution:

Costs function:

$$C(x) = \$42,500 + \$6,500 \times x$$

Revenue function:

a) Three customers per tour: $R_{1}(x) = \$3,500 \times 3x$

b) Two customers per tour: $R_{2}(x) = \$3,500 \times 2x$

Break-even volume:

a) in case the helicopter is filled to capacity:

$$\begin{array}{l} C(x) = R_{1}(x); \\ \$42,500 + \$6,500 \times x = \$3500 \times 3x; \\ \$4,000 \times x = \$42,500; \\ x = 10.625 \approx 11 \text{ tours} \end{array}$$

b) in case the helicopter carries two customers:

$$\begin{array}{l} C(x) = R_{2}(x); \\ \$42,500 + \$6,500 \times x = \$3500 \times 2x; \\ \$500 \times x = \$42,500; \\ x = 85 \text{ tours} \end{array}$$

Answer: 11 tours for the helicopter filled to capacity; 85 tours for the helicopter carrying two customers.