A consulting firm, using statistical methods, provided a veterinary clinic with the cost equation C(x) 0 00048(x 500) 3 60,000 100 x 1,000 where C(x) is the cost in dollars for handling x cases per month The average cost per case is given by C(x) C(x) x (A) Write the equation for the average cost f...

A consulting firm, using statistical methods, provided a veterinary clinic with the cost equation C(x) = 0.00048(x

Question:

A consulting firm, using statistical methods, provided a veterinary clinic with the cost equation

C(x) = 0.00048(x - 500)³ + 60,000
100 ≤ x ≤ 1,000

where C(x) is the cost in dollars for handling x cases per month. The average cost per case is given by
C̅(x) = C(x) / x.
(A) Write the equation for the average cost function C̅.
(B) Graph C̅ on a graphing calculator.
(C) Use an appropriate command to find the monthly caseload for the minimum average cost per case. What is the minimum average cost per case?

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