Question

The cost in dollars to manufacture x pairs of shoes is given by 12,000+19x. This month, the manufacturer produced 1000 more pairs of shoes than last month. The average cost per pair dropped by $0.43.

Write an expression for the average cost per pair of shoes.

Answer 1

The expression for the average cost per pair of shoes is;

12000/(1000+x) + 19 = 12000/x + 19 - 0.43

Cost per pair of shoe is $21.067

Explanation:

Here we have cost of x pair of shoes = 12000 + 19x

Therefore the average cost = 12000/x + 19

When x + 1000 is produced we have

x + 1000 = 12000 + 19(1000+x)

Therefore average cost = 12000/(1000+x) + 19

Therefore 12000/(1000+x) + 19 = 12000/x + 19 - 0.43

Therefore x = 4806.315 and we have

5806.3 = cost $ 122320

Which gives the cost per pair = $21.067.