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
