The total cost of producing a type of truck is given by C(x)=13000−60x+0.2x2, where x is the number of trucks produced. How many trucks should be produced to incur minimum cost?

Answer 1

take the derivative and set it equal to zero, then solve for x

C'(x) = -60 + 0.4x = 0

0.4 x = 60

x = 60/0.4 = 600/4 = 150 trucks for minimum cost

C(150) = 13,000-60(150) + 0.2(150)^2 =13,000 -9000 + (1/5)(22500) = 13,000-9,000 + 4,500= 8,500 = minimum cost