The total cost of producing a type of truck is given by C(x)=25000−80x+0.1x2, where x is the number of trucks produced. How many trucks should be produced to incur minimum cost?

Answer 1

C'(x) = -800+.2x =0

x = 800/.2 = 4000 trucks = output level with minimum cost

C(4000) = 25,000 -80(4000) + .1(4000)^2 =

25,000 - 32000 + 16000= 9,000 = minimum cost

take the derivative of the cost function and set it equal to zero and solve for x =4,000. plug x=4000 into the cost function to get the minimum cost