Optimal Cost Of Production

Question

A manufacturer finds that the cost C(x)=2x^2 - 8x + 15 , where x is the number of machine operating, find how many machines should one operate to minimize the total cost of production. what is the optimal cost of production?

Answer 1

Answer 2

2 machines

optimal is 7

Answer 3

C(x) = 2x^2 -8x +15

take the derivative and set equal to zero

C'(x) = 4x -8 =0

x = 8/4 = 2

C(2) = 2(4)-8(2)+15 = 7=y

cost minimizing output level = 2,

minimum cost= 7

2x^2 -8x +15

=2(x^2 -4x + 4) +15 -8

2(x-2)^2 + 7 in vertex form. vertex=minimum point = (2,7)=(x,C) where 2 = cost minimizing output,

7=minimal Cost

optimal Cost is when profits are maximum which depends on the revenue

max profits are when marginal cost = marginal revenue, MC=MR, C'=R', 4x-8=R'

if Marginal Revenue =0, the optimal cost = minimum Cost=7

but usually MR does not =0. you need to know the Revenue function to find optimal Cost