A supply company manufactures copy machines. The unit cost C (the cost in dollars to make each copy machine) depends on the number of machines made. If x machines are made, then the unit cost is given by the function

C (x) = 0.8x ^ 2 - 256x + 25,939. How many machines must be made to minimize the unit cost? Do not round your answer.

Number of copy machines:

Question

Mathematics

Everett Sutton

28 February, 06:31

A supply company manufactures copy machines. The unit cost C (the cost in dollars to make each copy machine) depends on the number of machines made. If x machines are made, then the unit cost is given by the function

C (x) = 0.8x ^ 2 - 256x + 25,939. How many machines must be made to minimize the unit cost? Do not round your answer.

Number of copy machines:

+4

Answers (1)

Know the Answer?

Roderick Mcdowell · Answer 1

To answer this item, we take the differential of the equation and equate to zero.

C (x) = 0.8x² - 256x + 25939

Differentiation,

dC (x) = 1.6x - 256

dC (x) = 1.6x - 256 = 0

The value of x from the derived equation above is 160.

Thus, the number of machine to be made in order to minimize the cost should be 160.