Suppose that a company needs 800 items during a year and that preparation for each production run costs $60. Suppose further that it costs $8 to produce each item and $0.45 to store an item for one year. Use the inventory cost model to find the number of items in each production run that will minimize the total costs of production and storage.
A)449 items
B)462 items
C)491 items
D)480 items
E)469 items

Question

Suppose that a company needs 800 items during a year and that preparation for each production run costs $60. Suppose further that it costs $8 to produce each item and $0.45 to store an item for one year. Use the inventory cost model to find the number of items in each production run that will minimize the total costs of production and storage. ​
A)449 items
B)462 items
C)491 items
D)480 items
E)469 items

Quizplus · Accepted Answer

Let x be the number of items in each production run.
Total relevant cost = (annual demand / x) * (preparation cost per run) + (x / 2) * (production cost per item) + (x / 2) * (storage cost per item)

Substituting the given values:

Total relevant cost = (800 / x) * 60 + (x / 2) * 8 + (x / 2) * 0.45

Total relevant cost = 4800 / x + 4x + 0.225x

To minimize the cost, we take the derivative of this expression with respect to x and set it equal to 0:

-4800 / x^2 + 4 + 0.225 = 0

Solving this equation:

x = 461.61

Rounding up to the nearest integer, we get x = 462.

Therefore, producing 462 items in each production run will minimize the total costs of production and storage.

Suppose That a Company Needs 800 Items During a Year