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University of Michigan, Dearborn *

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Feb 20, 2024

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1 IMSE 421 Homework 2 Name: Mnahil Syed QUESTION 1 (20 Points) Acme Sealants specializes in producing silicone sealants and is considering switching its production to a new non-silicone material. The factory currently produces 1000 sealants per day, which are sold for $6.75 each. The cost of producing each sealant is $3.75. If Acme decides to switch to using the new non- silicone material, they will be able to produce 500 units per day, selling each at a price of $10.00. The cost of producing each new sealant is $3.25. Acme can only produce one type of sealant at a time. Calculate the opportunity cost of switching from the silicone sealant to the new non-silicone material. Hint: Consider the daily profit from producing each type of gasket and the lost profit from the forgone production of silicone gaskets. Note: Profit = Quantity x (Selling Price - Cost of Production) Daily Profit from producing silicone sealants: Profit = 1000 x ($6.75 - $3.75) = $3000 Daily Profit from producing non-silicone sealants: Profit = 500 x ($10.00 - $3.25) = $3375 Opportunity Cost from switching from the silicone sealant to the new non-silicone sealant: $3000 - $3375 = -$375 (negative value indicates gain) The opportunity cost of switching to the non-silicone material is $375, so Acme Sealants would gain $375 per day by switching to new non-silicone material.

2 1 QUESTION 2 (35 points) Acme Storage totes in hardware stores where price and demand are related as shown below: p = $60 – 0.04D The fixed cost (C F ) is $3,500 per month and the variable cost per toolbox (c v ) is $35. a) How many totes should be produced each month to maximize profits? Provide an explanation. Maximizing Profits Formula: D * = (a – c v ) / 2b D * = ($60 – $35) / (2(0.04)) D * = 312.5 totes per month Since we can not produce half of a tote, we round up and produce 313 totes each month to maximize profits. b) How much is the maximum profit each month? Provide an explanation. Profit = - bD 2 + (a – c v )D – C f Profit = -0.04(313) 2 + ($60 - $35)(313) - $3,500 Profit = $406.24 The maximum profit is $406.24 if Acme Storage produces 313 totes.

3 QUESTION 3 (45 points) With reference to Acme Storage in Question 2, assume price and demand are unrelated. The company can sell the totes for $75 each if they spend $5,000 per month on advertising (C a ). C F and c v remain as indicated in the original question. The maximum production capacity is 1,000 units per month. a) What is the demand breakeven point? Provide an explanation. Demand Breakeven Point Formula: D′ = C F + C a / (p – c v ) D ’ = $3,500 + $5,000 / ($75 - $35) D ’ = 212.5 totes per month D ’ = 213 / 1,000 = 0.213 = 21.3% Since we cannot produce half a tote, we round up and produce 213 totes per month or 21.3% or capacity to break even. b) Is the company’s demand breakeven point (in %) more sensitive to a 10% increase in the sales price or a 20% reduction in the variable costs? Explain your answer. A 10% increase in sales price (p) gives: P = $75 + 7.5 = $82.50 D ’ = $3,500 + $5,000 / ($82.50 - $35) D ’ = 178.95 totes per month (213 – 179) / 213 = 0.1596 = 15.96% reduction in D ’ A 20% reduction in variable costs (C v ) gives: C v = $35 – 7 = $28 D ’ = $3,500 + $5,000 / ($75 - $28) D ’ = 180.85 totes per month (213 – 181) /213 = 0.1502 = 15.02% reduction in D ’ The demand breakeven point is more sensitive to the 10% increase in sales price rather than the 20% reduction in variable costs, because the higher increase in the selling price has a more significant impact on the breakeven quantity compared to a reduction in variable costs.

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