Question

Foggy​ Optics, Inc. makes laboratory microscopes. Setting up each production run costs $4500. Insurance​ costs, based on the average number of microscopes in the​ warehouse, amount to ​$20 per microscope per year. Storage​ costs, based on the maximum number of microscopes in the​ warehouse, amount to ​$20 per microscope per year. Suppose that the company expects to sell 2400 microscopes at a fairly uniform rate throughout the year. Determine the number of production runs that will minimize the overall expenses for the company.

Options:
A) 5 production runs
B) 6 production runs
C) 7 production runs
D) 8 production runs

Answer 1

To determine the number of production runs that will minimize costs for Foggy Optics, Inc., the setup cost for each run and the inventory-related insurance and storage costs must be considered. Calculating the total annual cost for each option (A to D) and choosing the one with the lowest cost will yield the optimal number of production runs.

Step-by-step explanation:

The question involves determining the optimal number of production runs for Foggy Optics, Inc., which manufactures laboratory microscopes. To minimize costs, one must consider the setup cost per production run and the ongoing costs for insurance and storage of the microscopes.

The total annual cost (TAC) can be calculated with the following components: setup cost, insurance cost, and storage cost. Setup cost is fixed at $4500 per production run, while insurance and storage costs depend on the average and maximum inventory levels respectively.

Given that there are 2400 microscopes sold uniformly throughout the year, the number of production runs will impact the inventory levels and in turn affect the insurance and storage costs.

The optimal number of production runs is found by examining the options provided (A to D), calculating the TAC for each, and selecting the one with the lowest cost. The formula for TAC in this scenario is:

TAC = (Number of Production Runs × $4500) + (Average Inventory Level × $20) + (Maximum Inventory Level × $20)

Where Average Inventory Level = (2400 / Number of Production Runs) / 2
and Maximum Inventory Level = 2400 / Number of Production Runs

After performing these calculations, we can determine which option minimizes the TAC and thus, the optimal number of production runs.