Help with Optimization and Decision Support Modeling for Business HW2

OSCM 471/571 Optimization and Decision Support Modeling for Business

Homework 2, Spring 2023

Notice for Homework 2

Instructor: Seokjun Youn ( [email protected] )

· Due date: Thursday 2/16, 11:59 pm

· Please submit your files to D2L > Assignments > Homework 2

1. A Word file (or PDF) with your answers combined into a single document.

2. An Excel spreadsheet template with your answers (for some sub-questions).

· This homework is made up of FIVE questions (20 pts):

· Q1: 3 sub-questions (2 pts)

· Q2: 3 sub-questions (5 pts)

· Q3: 2 sub-questions (5 pts)

· Q4: 1 question (4 pts)

· Q5: 1 question (4 pts)

· Students may choose either handwriting or word processing (or both).

· Handwriting: please properly scan or take photos and organize them into one file before uploading in D2L.

· Please write down your solutions step-by-step for partial credit.

· You may use:

· Your textbook and notes from the class.

· Notes or sources from a related class or internet source.

· Discussion with the instructor.

· Voluntary, mutual, and cooperative discussion with other students currently taking the class.

· You may not use:

· Solution manuals (printed or electronic).

· Copying from other students in this class, including expecting them to reveal their solutions in “discussion.”

· It is fine if your answer is not 100% correct. However, if you do not put enough effort to the assignment, your score for this homework will be lower than your expectation. So, please try to convince your logic to instructor.

Your Name:

1. The shaded area in the following graph represents the feasible region of a linear programming problem whose objective function is to be maximized, where x1 and x2 represent the level of the two activities.

Label each of the following statements as True or False, and then justify your answer based on the graphical method. In each case, give an example of an objective function that illustrates your answer.

a. If (3,3) produces a larger value of the objective function than (0, 2) and (6, 3), then (3, 3) must be an optimal solution.

Answer:

b. If (3, 3) is an optimal solution and multiple optimal solutions exist, then either (0, 2) or (6, 3) must also be an optimal solution.

Answer:

c. The point (0, 0) cannot be an optimal solution.

Answer:

2. Larry Edison is the director of the Computer Center for Buckly College. He now needs to schedule the staffing of the center. It is open from 8 am until midnight. Larry has monitored the usage of the center at various times of the day and determined that the following number of computer consultants are required.

Two types of computer consultants can be hired: full-time and part-time. The full-time consultants work for eight consecutive hours in any of the following shifts: morning (8 am –4 pm), afternoon (noon–8 pm), and evening (4 pm –midnight). Full-time consultants are paid $14 per hour.

Part-time consultants can be hired to work any of the four shifts listed in the table. Part-time consultants are paid $12 per hour.

An additional requirement is that during every time period, there must be at least two full-time consultants on duty for every part-time consultant on duty.

Larry would like to determine how many full-time and part-time consultants should work each shift to meet the above requirements at the minimum possible cost.

a. Which category of linear programming problem does this problem fit? Why?

Answer:

b. Formulate and solve a linear programming model for this problem on a spreadsheet.

· Please include the screenshot of your final spreadsheet model here.

Answer:

c. Summarize the model in algebraic form.

Answer:

3. The Weigelt Corporation has three branch plants with excess production capacity. Fortunately, the corporation has a new product ready to begin production, and all three plants have this capability, so some of the excess capacity can be used in this way. This product can be made in three sizes—large, medium, and small—that yield a net unit profit of $420, $360, and $300, respectively. Plants 1, 2, and 3 have the excess capacity to produce 750, 900, and 450 units per day of this product, respectively, regardless of the size or combination of sizes involved.

The amount of available in-process storage space also imposes a limitation on the production rates of the new product. Plants 1, 2, and 3 have 13,000, 12,000, and 5,000 square feet, respectively, of in-process storage space available for a day’s production of this product. Each unit of the large, medium, and small sizes produced per day requires 20, 15, and 12 square feet, respectively.

Sales forecasts indicate that if available, 900, 1,200, and 750 units of the large, medium, and small sizes, respectively, would be sold per day.

At each plant, some employees will need to be laid off unless most of the plant’s excess production capacity can be used to produce the new product. To avoid layoffs if possible, management has decided that the plants should use the same percentage of their excess capacity to produce the new product.

Management wishes to know how much of each of the sizes should be produced by each of the plants to maximize profit.

a. Formulate and solve a linear programming model for this mixed problem on a spreadsheet.

· Please include the screenshot of your final spreadsheet model here.

Answer:

b. Express the model in algebraic form.

Answer:

4. The Cost-Less Corp. supplies its four retail outlets from its four plants. The shipping cost per shipment from each plant to each retail outlet is given below.

Plants 1, 2, 3, and 4 make 10, 20, 20, and 10 shipments per month, respectively. Retail outlets 1, 2, 3, and 4 need to receive 20, 10, 10, and 20 shipments per month, respectively.

The distribution manager, Randy Smith, now wants to determine the best plan for how many shipments to send from each plant to the respective retail outlets each month. Randy’s objective is to minimize the total shipping cost.

Formulate this problem as a transportation problem on a spreadsheet and then use Solver to obtain an optimal solution.

a. Please include the screenshot of your final spreadsheet model here.

Answer:

5. Four cargo ships will be used for shipping goods from one port to four other ports (labeled 1, 2, 3, 4). Any ship can be used for making any one of these four trips. However, because of differences in the ships and cargoes, the total cost of loading, transporting, and unloading the goods for the different ship–port combinations varies considerably, as shown in the following table.

The objective is to assign the four ships to four different ports in such a way as to minimize the total cost for all four shipments. Formulate and solve this problem on a spreadsheet.

a. Please include the screenshot of your final spreadsheet model here.

Answer:

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