The equation for the cost in dollars of producing automobile tires is c = 0.15x2 - 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

Number of tires = 1000
Minimum cost = 20