Radon Research Corporation RRC)is one of 24 firms in Albuquerque testing homes for dangerous levels of radon gas.There is a standard test that all testing companies use.The manager of RRC wants to know the number of homes to test in 2015 in order to maximize the firm's profit.The manager forecasted a price of $160 for radon tests in 2015.The firm's marginal cost was estimated as where Q is the number of tests performed each week.RRC's fixed cost will be $250 per week.The average variable cost at RRC is

Question

Radon Research Corporation RRC)is one of 24 firms in Albuquerque testing homes for dangerous levels of radon gas.There is a standard test that all testing companies use.The manager of RRC wants to know the number of homes to test in 2015 in order to maximize the firm's profit.The manager forecasted a price of $160 for radon tests in 2015.The firm's marginal cost was estimated as  where Q is the number of tests performed each week.RRC's fixed cost will be $250 per week.The average variable cost at RRC is

Quizplus · Accepted Answer

To maximize the profit, the firm needs to produce where marginal cost equals marginal revenue. In this case, the manager has forecasted a price of $160 for radon tests in 2015. So, the marginal revenue (MR) is $160.

Therefore, to find the optimal number of tests to perform, we need to set MR = MC, where MC is the marginal cost function.
160 = 7.5Q + 0.2667Q^2
0.2667Q^2 + 7.5Q - 160 = 0

Solving the quadratic equation above, we get:
Q = 54.72 or Q = -285.72

Since the number of tests cannot be negative, the optimal number of tests to perform is Q = 54.72 tests.

To find the average variable cost (AVC), we need to divide the total variable cost (TVC) by the number of tests (Q).
TVC = MC * Q
TVC = (0.2667Q^2 + 7.5Q) * Q
TVC = 0.2667Q^3 + 7.5Q^2

AVC = TVC / Q
AVC = (0.2667Q^3 + 7.5Q^2) / Q
AVC = 0.2667Q^2 + 7.5Q

Plugging in Q = 54.72, we get:
AVC = 0.2667(54.72)^2 + 7.5(54.72)
AVC = $18.87 per test

Therefore, the best choice is D, which gives an average variable cost of $18.87 per test at the optimal number of tests to perform.

Radon Research Corporation RRC)is One of 24 Firms in Albuquerque