Foggy optics, inc. makes laboratory microscopes. setting up each production run costs $2500. 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 $15 per microscope per year. suppose that the company expects to sell 1600 microscopes at a fairly uniform rate throughout the year, determine the number of production runs that will minimize the company's overall expenses.
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To determine the number of production runs that will minimize the company's overall expenses, we need to find the optimal production quantity.
Let's break down the steps:
Step 1: Calculate the annual holding cost per microscope.
The holding cost per microscope includes both insurance and storage costs.
Holding cost per microscope = Insurance cost + Storage cost
= $20 + $15 per microscope per year
= $35 per microscope per year
Step 2: Calculate the number of production runs needed to meet the expected sales.
Total production runs = (Total microscopes needed / Microscopes per production run)
Microscopes per production run can be calculated using the Economic Order Quantity (EOQ) formula:
EOQ = √((2 * annual demand * setup cost) / holding cost per microscope)
Given:
Annual demand = 1600 microscopes
Setup cost = $2500
Holding cost per microscope = $35
Microscopes per production run = EOQ
= √((2 * 1600 * 2500) / 35)
Step 3: Calculate the number of production runs needed.
Total production runs = (Total microscopes needed / Microscopes per production run)
= 1600 / Microscopes per production run
Substituting the calculated value of Microscopes per production run:
Total production runs = 1600 / (√((2 * 1600 * 2500) / 35))
Calculating this expression will give us the number of production runs that will minimize the company's overall expenses.
Please note that the final answer may involve rounding up or down depending on the company's policies or practical considerations.
To determine the number of production runs that will minimize the company's overall expenses, we need to calculate the total expenses for each possible number of production runs and then identify the number of runs with the lowest total expense.
Let's break down the expenses for each production run:
1. Production setup costs: $2500 per run.
2. Insurance costs: $20 per microscope per year. Since the company expects to sell 1600 microscopes, the average number of microscopes in the warehouse would be half of this amount, i.e., 1600/2 = 800 microscopes.
Total insurance cost = $20/microscope * 800 microscopes = $16,000 per year.
3. Storage costs: $15 per microscope per year. The maximum number of microscopes in the warehouse would be equal to the number of microscopes the company expects to sell in a year, i.e., 1600 microscopes.
Total storage cost = $15/microscope * 1600 microscopes = $24,000 per year.
Now, let's calculate the total expenses for different numbers of production runs:
1. For 1 production run:
Total expenses = Production setup costs + Insurance costs + Storage costs
= $2500 + $16,000 + $24,000 = $42,500 per year.
2. For 2 production runs:
Total expenses = 2 * Production setup costs + Insurance costs + Storage costs
= 2 * $2500 + $16,000 + $24,000 = $45,000 per year.
3. For 3 production runs:
Total expenses = 3 * Production setup costs + Insurance costs + Storage costs
= 3 * $2500 + $16,000 + $24,000 = $47,500 per year.
4. Continue this calculation pattern until you reach a reasonable number of production runs.
Compare the total expenses for different numbers of production runs and identify the number of runs with the lowest total expense. In this case, it would require calculating the expenses for a few more runs to find the minimum.