lp computer solution problems
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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.
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