For this discussion topic each student is required to have at least 2 postings: One answering at least one of the questions and a second responding to another student’s posting. Please select a question that has not been answered by the time you post your response. You can select any question to answer once all questions are answered. Please do not copy another student’s posting.

This discussion will close at midnight Sunday, October 7^th.

1. Explain the primary differences between a software package such as QM for Windows and Excel spreadsheets for solving linear programming problems.

2. Find the optimal solution of the following linear programming problem using QM for Windows or Excel.

Minimize 2x + 2y

Subject to

x + y > 5

x + 2y < 8

x, y > 0

3. Write the following problem in the required format for QM for Windows. Do NOT solve the problem.

Maximize 4x + 5y

Subject to

(2/3)x + (1/2)y > 20

x – 30 < 2y

x, y > 0

4. Southern Sporting Goods Company makes basketballs and footballs. Each product is produced from two resources—rubber and leather. The resource requirements for each product and the total resources available are as follows:

Resource Requirements per Unit

Product Rubber (lb.) Leather (ft.²)

Basketball 3 4

Football 2 5

Total resources available 500 lb. 800 ft.²

Each basketball produced results in a profit of $12, and each football earns $16 in profit.

I have formulated and solved the problem by using QM for Windows. The output from QM for Windows is displayed below.

Linear Programming Results:

Basketball Football RHS Dual

Maximize 12 16

Rubber 3 2 <= 500 0

Leather 4 5 <= 800 3.2

Solution-> 0 160 Optimal Z-> 2,560

Solution List:

Variable Status Value

Basketball NONBasic 0

Football Basic 160

slack 1 Basic 180

slack 2 NONBasic 0

Optimal Value (Z) 2560

(a) Determine the optimal solution from the output from QM for Windows.

(b) Make a recommendation to the company based on the output from QM for Windows.

5. A company produces two products, A and B, which have profits of $9 and $7, respectively. Each unit of product must be processed on two assembly lines, where the required production times are as follows.

Hours/Unit

Product Line 1 Line 2

A 12 4

B 4 8

Total hours 60 40

I have formulated and solved the problem by using Excel. The results are given below.

Problem 5
Variable		Product A	Product B
Profit		9	7
Constraints					Used	Slack
Line 1		12	4	60	60	-4E-10
Line 2		4	8	40	40	-6E-10
Variable		Value
Product A		4
Product B		3
Total Profit		57

Answer Report:

Microsoft Excel 11.0 Answer Report
Worksheet: [Problem 5.xls]Sheet1
Report Created: 8/20/2018 1:10:00 PM
Target Cell (Max)
	Cell	Name	Original Value	Final Value
	$C$12	Total Profit Value	0	57
Adjustable Cells
	Cell	Name	Original Value	Final Value
	$C$10	Product A Value	0	4
	$C$11	Product B Value	0	3
Constraints
	Cell	Name	Cell Value	Formula	Status	Slack
	$F$6	Line 1 Used	60	$F$6<=$E$6	Binding	0
	$F$7	Line 2 Used	40	$F$7<=$E$7	Binding	0

(a) Determine the optimal solution from the output from Excel.

(b) Make a recommendation to the company based on the output from Excel.