A medical equipment industry manufactures X-ray machines. The unit cost c
(the cost in dollars to make each X-ray machine) depends on the number of machines made. If x machines are made, then the unit cost is given by the function
c(x)=x^2-520x+72857. What is the minimum unit cost?
Do not round your answer

The minimum unit cost is $5257

Step-by-step explanation:

Minimization

Given a function c(x), the minimum value of c can be found by computing the first derivative. Equating the first derivative to zero will provide the critical points, or candidate point to maximize or minimize the function. The second derivative criterion will make clear which type of point was obtained.

The cost in dollars to produce x machines is

Find the first derivative

Equate to 0

Solving:

There must be produced 260 machines to minimize the cost. The minimum cost is

The minimum unit cost is $5257

594 square inches

step-by-step explanation:

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