Problem 1 (25 Points) Davison Electronics manufactures three LED television monitors, identified as Model A, Model B, and Model C. Davison Electronics four manufacturing plants. Each model has its lowest possible production cost when produced at Plant 1. However, Plant 1 does not have the capacity to handle the total production of all three models. As a result, at least some of the production must be routed to the other manufacturing plants. The following table shows the minimum production requirements for next month, the plant capacities in units per month, and the production cost per unit at each plant: Production Cost per Unit Minimum Model Plant 1 Plant 2 Plant 3 Plant 4 Production Requirements A $25 $28 $37 $34 48,000 B $26 $35 $36 $41 75,000 C $20 $31 $26 $23 60,000 65,000 50,000 32,000 43,000 Production Capacity Davison's objective is to determine the cost-minimizing production plan. 1. (10 Points) Please formulate the problem as a linear optimization model. Please include the complete mathematical model formulation in a new worksheet and call it as "Problem 1". Please note that an Excel worksheet is not a substitute for the mathematical formulation. (If you prefer, you can write down the model clearly on a piece of paper, take a picture of it, and then insert the picture into the Excel spreadsheet.) 2. (10 Points) Please solve the linear program formulated in Part 1 using Excel solver. Set up a spreadsheet to represent your mathematical model and rename it as "Solution 1". As part of solver's solution, please include both Answer Report and Sensitivity Report. You can keep the names of these two reports that Excel gives them. 3. (5 Points) Please use the information in Excel's Answer Report to answer the following questions and include all the answers in an orderly fashion in the worksheet Solution 1. a. What is the cost-minimizing production plan? What is the minimal production cost? b. Which constraints are binding?

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter5: Network Models

Section5.3: Assignment Models

Problem 10P

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Davison Electronics manufactures three LED television monitors, identified as Model A, Model B, and Model C. Davison Electronics four manufacturing plants. Each model has its lowest possible production cost when produced at Plant 1. However, Plant 1 does not have the capacity to handle the total production of all three models. As a result, at least some of the production must be routed to the other manufacturing plants. The following table shows the minimum production requirements for next month, the plant capacities in units per month, and the production cost per unit at each plant:

Model	Production Cost per Unit	Minimum Production Requirements
Plant 1	Plant 2	Plant 3	Plant 4
A	$25	$28	$37	$34	48,000
B	$26	$35	$36	$41	75,000
C	$20	$31	$26	$23	60,000
Production Capacity	65,000	50,000	32,000	43,000