HW 8_Ch 12 (1)

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Arizona State University *

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Industrial Engineering

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Apr 3, 2024

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LP ASSIGNMENT Please follow the instructions below and complete the assignment. Once you have the mathematical formulations, you will have to solve the problems in Excel and submit your answers in a quiz on Classes. 1. Homework (Not to Submit) Formulate the following 6 problems using the three steps from the lecture. Make sure to write down constraints in a linear format. Ch. 12: A, B, 2, 9 Note: Problems A and B are not in the book and are stated below. The other problems are at the end of Ch. 12 in your textbook. 2. Check the solution The correct models/formulations are given in the accompanying pdf file, LP Formulation Soln, on Classes. Check your answers against the given models once you have formulated the models. Please make sure to do it yourself before checking the solution. After making sure your formulation is correct, proceed to solving the problems in Excel. Homework Problem not in the Textbook Ch12-A As a part of quality improvement initiative, United Technologies employees must complete a four-day training program on team building and a three-day training program on problem solving. The manager has requested that at least 8 training programs on team building and at least 10 training programs on problem solving be offered during the next six months. In addition, senior-level management has specified that at least 25 training programs must be offered during this period. United Technologies uses a consultant to teach the training programs. During the next 6 months, the consultant has 84 days of training time available. Each training program on team building costs $8,000 and each training program on problem solving costs $6,000. (a) Formulate a linear programming model that can be used to determine the number of training programs on team building and the number of training programs on problem solving that should be offered in order to minimize total cost. (b) Solve the problem using Excel Solver. What are the optimal solution and the minimum total cost? [Hint: you should get optimal objective value = $166,000.] (c) In 12-A(a), suppose the following changes are made.  United Technologies (UT) must offer 3-day training program on time management, at a cost of $5,000 each , in addition to the two programs mentioned in the problem.  It must offer at least 16 of the time management programs during the next 6 months.  Fortunately, UT was able to hire one additional consultant who has 84 days available , effectively doubling the total available training time. Solve this new problem. Ch12-B The Big Bang Novelty Company (BBNC) makes 3 types of noise - makers: Toot, Wheet, and Honk. A Toot can be made in 30 minutes and has a feather attached to it. A Wheet requires 20 minutes, has two feathers, and is sprinkled with 0.5 ounces of sequin powder. The Honk requires 30 minutes, three feathers, and 1 ounce of sequin powder. The unit profits are $0.90 per Toot, $1.10 per Wheet, and $1.40 per Honk. The following resources are available: 100 hours of labor, 400 feathers, and 80 ounces of sequi n powder. 1
BBNC would like to maximize the overall profit from the noise-makers. (a) Write the linear programming model. Express labor time in minutes in LP formulation. (b) Solve using Excel Solver. What are the optimal solution and the maximum total profit? (c) How much of the resources (labor, feathers, and sequin powder) will be used by the optimal solution? (d) If the availability of labor increases by 10 hours, what is the optimal total profit? (e)Suppose Big Bang decides they will start adding 0.2 oz of sequin powder to Toots.  (Assume the labor availability is back at the original 100 hours.) What is the new optimal solution? 2
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