Find the change in annual cost when Q is increased from 356 to 357, and compare this with the instantaneous rate of change when Q = 356.

Question

The annual inventory cost C for a manufacturer is given below, where Q is the order size when the inventory is replenished. Find the change in annual cost when Q is increased from 356 to 357, and compare this with the instantaneous rate of change when Q = 356. (Round your answers to two decimal places.)

C = (1,020,000/Q ) +7.6Q

Change in C=

C''(356) =

Answer 1

Hi Celine, the change in C can be calculated by evaluating the cost function at Q = 356 and Q = 357

change in C = 1,020,000/357 + 7.6*357 - 1,020,000/356 + 7.6*356 ≈ -0.43

Instantaneous rate of change in C is first order derivative C':

C'(Q) = -1,020,000/(Q^2) + 7.6

C'(356) = -1,020,000/(356^2) + 7.6 ≈ - 0.45

Hope my answer helps.