# linar optimization techniques

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The purpose of this assignment is to employ linear optimization techniques, interpret results, and determine optimal solutions for business problems.

Using specified data files, chapter example files, and templates from the “Topic 4 Student Data, Template, and Example Files” topic material, complete Chapter 13, Problems 25 (part a), 28 (part a), 31 (part a), 32 (part a), and 37 (part a) from the textbook. Use Microsoft Excel’s Solver Add-In to complete these problems. For each of these problems, run the Solver’s Answer and Sensitivity Reports. Interpret and summarize the key results.

To receive full credit on the assignment, complete the following.

- Ensure that all Solver settings are defined through the use of the Solver dialog box.
- Ensure that Excel files include the associated cell functions and/or formulas if functions and/or formulas are used.
- Include a written response to all narrative questions presented in the problem by placing it in the associated Excel file.
- Include Answer and Sensitivity Reports interpretation and summary of key results.
- Place each problem in its own Excel file. Ensure that your first and last name are in your Excel file names.

APA style is not required, but solid academic writing is expected.

This assignment uses a rubric. Please review the rubric prior to beginning the assignment to become familiar with the expectations for successful completion. 25 (part a)-A chemical company manufactures three chemicals: A, B, and C. These chemicals are produced via two production processes 1 and 2. Running process 1 for an hour costs $400 and yields 300 units of A, 100units of B, and 100 units of c, Running process for 2 an hour costs $100 and yields 100 units of A and 100units of B. To meet customer demands, at least 1000units of A, 500 units of B, and 300 units of C must be produced daily.a.Use Solver to determine a daily production plan that minimizes the cost of meeting the company’s daily demands. 28(part a)-During the next four months, a customer requires, respectively, 500, 650, 1000, and 700 units of a commodity, and no backlogging is allowed (that is, the customer’s requirements must be met on time). Production costs are $50, $80, $40, and $70 per unit during these months. The storage cost from one month to the next is $20 per unit (assessed on ending inventory). It is estimated that each unit on hand at the end of month 4 can be sold for $60. Assume there is no beginning inventory.a.Determine how to minimize the net cost incurred in meeting the demands for the next four months. 31(part a)-For a telephone survey, a marketing research group needs to contact at least 600 wives, 480 husbands, 400 single adult males, and 440 single adult females. It costs $3 to make a daytime call and (because of higher labor costs) $5 to make an evening call. The file P13_31.xlsx lists the results that can be expected. For example, 30% of all daytime calls are answered by a wife, 15% of all evening calls are answered by a single male, and 40% of all daytime calls are not answered at all. Due to limited staff, at most 40% of all phone calls can be evening calls.a.Determine how to minimize the cost of completing the survey.

Question1-Many times, linear optimization is used to maximize an objective function because profit, productivity, or efficiency is the outcome of interest. Provide two examples where the goal is to optimize a process by minimizing an objective function. In your examples, identify the outcome and any constraints that would need to be met. QUESTION 2-When many constraints are present in a linear optimization problem, there is a greater chance that a redundant constraint exists. Assume you are trying to maximize an objective function and you have two decision variables, X_{1} and X_{2}. If a redundant constraint exists, does the constraint become necessary if you try to minimize (instead of maximize) the same objective function? Why? Do you need an objective function to determine if a constraint is redundant? Explain. 32 (part a)-A furniture company manufactures tables and chairs. Each table and chair must be made entirely out of oak or entirely out of pine. A total of 15,000 board feet of oak and 21,000 board feet of pine are available. A table requires either 17 board feet of oak or 30 board feet of pine, and a chair requires either 5 board feet of oak or 13 board feet of pine. Each table can be sold for $800, and each chair for $300.a.Determine how the company can maximize its revenue. 37 (part a)-37.A company that builds sailboats wants to determine how many sailboats to build during each of the next four quarters. The demand during each of the next four quarters is as follows: first quarter, 160 sailboats; sec-ond quarter, 240 sailboats; third quarter, 300 sailboats; fourth quarter, 100 sailboats. The company must meet demands on time. At the beginning of the first quarter, the company has an inventory of 40 sailboats. At the beginning of each quarter, the company must decide how many sailboats to build during that quarter. For simplicity, assume that sailboats built during a quarter can be used to meet demand for that quarter. During each quarter, the company can build up to 160 sailboats with regular-time labor at a total cost of $1600 per sailboat. By having employees work overtime during a quarter, the company can build additional sailboats with overtime labor at a total cost of $1800 per sailboat. At the end of each quarter (after production has occurred and the current quarter’s demand has been satisfied), a holding cost of $80 per sailboat is incurred.a.Determine a production schedule to minimize the sum of production and inventory holding costs during the next four quarters.

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