The equation for the cost in dollars of producing automobile tires is c = 0.000015x2 - 0.03x + 35, where x is the number of tires produced. find the number of tires that minimizes this cost. what is the cost for that number of tires?

The cost function is

c = 0.000015x² - 0.03x + 35

where x = number of tires.

To find the value of x that minimizes cost, the derivative of c with respect to x should be zero. Therefore

0.000015*2x - 0.03 = 0

0.00003x = 0.03

x = 1000

Note:

The second derivative of c with respect to x is positive ( = 0.00003), so the value for x will yield the minimum value.

The minimum cost is

Cmin = 0.000015*1000² - 0.03*1000 + 35

= 20

Answer:

Number of tires = 1000

Minimum cost = 20