Question

A company has two factories, factory A and factory B. The cost per item to produce q items in factory A is

200 + 3/q
q
. The cost per item to produce q items in factory B is
300 + q/
3q
. Find an expression for the sum of these costs per item. Then divide this expression by 2 to find an expression for the average cost per item to produce q items in each factory.

The average cost per item to produce q items in each factory is

Answer 1

• (700 + 51q)/4q

Explanation:

Given costs:

• (200 + 13q)/q and (300 + 25q)/2q

Sum of the costs:

• (200 + 13q)/q + (300 + 25q/2q) =
• (400 + 26q)/2q + (300 + 25q)/2q =
• (700 + 51q)/2q

Average cost is sum divided by number:

• (700 + 51q)/2q ÷ 2 =
• (700 + 51q)/4q