# 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 2) If the unit profit of the Model 2 decreases to \$250 per unit, how would the optimal solution change?

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

(a) Decision Variables:

Here, Model1 and Model2 are the two types of roll bars that Wilson Industries need to produce.
Objective function

Max 200 Model1 + 280 Model2

Constraints:

20 Model1 + 25 Model2 ≤ 40,000 (Steel availability constraint)

40 Model1 + 100 Model2 ≤120,000 (Manufacturing time constraint)

60 Model1 + 40 Model2 ≤ 96,000 (Assembly time constraint)

Model1, Model2 ≥ 0

Optimal solution

Using the solver as shown below,

The solution to the linear programming problem

 Model1 Model2 Numbers 1000 800

Total profit = 1000 * 200 + 800 * 280 = \$424,000

(b) Decreasing the profit of Model2:

If the unit profit of the Model 2 decreases to \$250 per unit, how would the optimal solution change?

Revised solution with Model 2 profit of \$250 as shown below,

 Model1 Model2 Numbers 1143 686

Revised total profit = 1143 * 200 + 686 * 250 = \$400,000

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