Question

A manufacturer has determined that the total cost C of operating a factory is

Answer 1

Answer:

x = 100 units

Step-by-step explanation:

C = 2.5x^2 + 75x + 25000

To find average cost per unit, divide C by x:

C/x or Average cost (AC) per unit = $\frac{2.5x^2 + 75x + 25000}{x}$ = 2.5x + 75 + 25000/x ⇔ 2.5x + 75 + 25000x^-1 (equation 1)

To find cost minimising, we use differentiation (differentiate equation 1 in respect to x and set it equal to 0):

d(AC)/dx = 0

d(AC)/dx ⇔ 2.5 - 25000x^-2 = 0

2.5 = 25000x^-2

2.5 = $\frac{25000}{x^2}$

2.5x^2 = 25000

x^2 = 10000

x = $\sqrt{10000}$

x = 100 units