# Answered Essay: Problem Statement: The Charger Club of America sponsors driver education events that provide high-performance

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 at most 40,000 pounds of the high-alloy steel will be available next quarter. In addition, Wilson estimates that 2000 hours of manufacturing time and 1600 hours of 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 programming model 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 4) How much should the company be willing to pay to acquire additional ‘Steel’? Explain in detail.

Number to Make Unit Profits Constraints Steel available Manufacturing minutes Assembly minutes Model 1 \$200 600 Model 2 \$280 100 40 Total Profit Used Available 40,000 120,000 96,000

## Expert Answer

Spreadsheet model and Solution of the problem using excel solver is as follows

Optimal solution, Model 1 = 1000, Model 2 = 800

Question 4) The shadow price of steel is 8.8 (refer sensitivity report as below). Shadow price is the amount of profit that the compay generates from utilizing each additional pound of steel.

Therefore the company should be willing to pay \$ 8.8 per pound to acquire additional steel.

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