A vehicle factory manufactures cars. The unit cost C (the cost in dollars to make each car) depends on the number of cars made. If x cars are made, then the unit cost is given by the function C(x) = x^2 - 400x + 45,377 . What is the minimum unit cost?Do not round your answer.

Accepted Solution

Answer:5377Step-by-step explanation: C(x) = x^2 - 400x + 45,377 To find the location of the minimum, we take the derivative of the functionWe know that is a minimum since the parabola opens upwarddC/dx = 2x - 400We set that equal to zero2x-400 =0Solving for x2x-400+400=4002x=400Dividing by22x/2=400/2x=200The location of the minimum is at x=200The value is found by substituting x back into the equationC(200) = (200)^2 - 400(200) + 45,377            =40000 - 80000+45377             =5377