Problem Statement: The Charger Club of America sponsors driver education events that provide high-performance driving instruction on actual race tracks. Because safety is a primary consideration at such events, many owners elect to install roll bars in their cars. Wilson Industries manufactures two types of roll bars for Chargers, Model 1 and Model 2. Model 1 requires 20 pounds of a special high alloy steel, 40 minutes of manufacturing time, and 60 minutes of assembly time. Model 2 requires 25 pounds of the special high alloy steel, 100 minutes of manufacturing time, and 40 minutes of assembly time. Wilson's steel supplier indicated that atmost 40,000 pounds of the high-alloy steel will be available next quarter. Inaddition, Wilson estimates that 2000 hours of manufacturing time and 1600 hoursof assembly time will be available next quarter. The profit contributions are$200 per unit for Model 1 and $280 per unit for Model 2. The linear programmingmodel for this problem is as follows:
Variables:
Model1 = Number of Model 1 to produce
Model2 = Number of Model 2 to produce
Objective:
Max 200 Model1 + 280 Model2
Constraints subject to:
20 Model1 + 25 Model2 < 40,000 Steel available 40 Model1 + 100 Model2 < 120,000 Manufacturing minutes 60 Model1 + 40 Model2 < 96,000 Assembly minutes
Model1, Model2 > 0
Question 1) What are the optimal solution and the total profit?
Question 2) If the unit profit of the Model 2 decreases to $250 per unit, how would the optimal solution change?
Question 3) How much should the company be willing to pay to acquire additional capacity in the 'Assembly minutes' area? Explain in detail.
Question 4) How much should the company be willing to pay to acquire additional 'Steel'? Explain in detail.
Question 5) How much will the objective function, 'Total Profit', change if there was one additiional hour of Manufacturing capacity available?