Question

A jeweler wants to minimize business costs and has found that the average cost in dollars per necklace is given by C(x)=0.5x^2-7x+65.5, where x is the number of necklaces that are created.

Answer 1

The maximum cost is 41 dollars per necklace.

Explanation:

The average cost in dollars/necklace is given by :

`C(x)=0.5x^2-7x+65.5` .....(1)

Where

x is the number of necklaces that are created

To maximize the cost, find the value of x by putting dC/dx = 0

`(d)/(dx)(0.5x^2-7x+65.5)=0\\\\x-7=0\\\\x=7`

Now put the value of x = 7 in equation (1).

`C(x)=0.5(7)^2-7(7)+65.5\\\\=41\ \text{dollars per necklace}`

Hence, the maximum cost is 41 dollars per necklace.