3- Firestone has an option to produce five types of tires. Each of these tires r

Question

3- Firestone has an option to produce five types of tires. Each of these tires requires to pass three main tests on different stations. The first test station is available for 100 hours per week. The second and third stations are available for 110 hours per week. According to the good reputation of Firestone, the manager believes that the company can sell as many tires as it can manufacture. The variable labor costs are $14 per hour for station 1, $11 per hour for station 2, and $13 per hour for station 3. Use the following sensitivity report for maximizing the profit of this LP model to answer the following question. (Required test times, revenue and cost information are shown in the following table)

Use a pricing out strategy to find the selling price for this brand new tire, which would make the tire attractive to be in the Firestone production plan (The profit maximization problem is already solved and the sensitivity report from the solution Excel file is given to you).

All season 3 minutes 3.7 minutes2.5 minutes 2.9 minutes 5 minutes 3.7 minutes ChampionDestination Firehawk Transforce Tire Model Station 1 Station2 Station 3 Tire selling price Material cost per tire 2 minutes 3 minutes 2.5 minutes 2.5 minutes 2.7 minutes 3.7 minutes $65 4 minutes 4 minutes 3 minutes $68 S60 S68 $60 $32 $29 $30 $28 S30

Explanation / Answer

Looking at the sensitivity report, we see that station # 2 and 3 are binding constraints (bottleneck resources)

Tire model Destination takes lesser time on station 2 as compared to the New tire type. So new tire's profit per minute of station 2 has to be at least equal or more than the profit per minute of Destination on station 2, which is (68-30)/2.9 = 13.10

Therefore, minimum selling price of new tire should be = 30+13.10*3 = $ 69.31

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