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(a) Model the problem of maximizing next months profit as a linear program and solve it. Report both your LP and optimal solution in your submission. (b) Find the Shadow Price of each of the three processes as they relate to your optimal solution and report them here. Describe how you found the prices and identify the units for each price. (c) Management is considering hiring some extra inspection time, but the union requires that inspectors are paid $12 per hour. Will it be profitable to hire another man-hour of inspection capacit at a price of 12 dollars? How do you know? (d) At what price would should be willing to rent 1 machine-hour of vibration to a competing producer? How many machine-hours can be rented out before your optimal solution changes.

(a) Model the problem of maximizing next months profit as a linear program and solve it. Report both your LP and optimal solution in your submission. (b) Find the Shadow Price of each of the three processes as they relate to your optimal solution and report them here. Describe how you found the prices and identify the units for each price. (c) Management is considering hiring some extra inspection time, but the union requires that inspectors are paid $12 per hour. Will it be profitable to hire another man-hour of inspection capacit at a price of 12 dollars? How do you know? (d) At what price would should be willing to rent 1 machine-hour of vibration to a competing producer? How many machine-hours can be rented out before your optimal solution changes.

Practical Management Science
Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter2: Introduction To Spreadsheet Modeling
Section: Chapter Questions
Problem 20P: Julie James is opening a lemonade stand. She believes the fixed cost per week of running the stand...
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(a) Model the problem of maximizing next months profit as a linear program and solve it. Report
both your LP and optimal solution in your submission.

(b) Find the Shadow Price of each of the three processes as they relate to your optimal solution
and report them here. Describe how you found the prices and identify the units for each price.

(c) Management is considering hiring some extra inspection time, but the union requires that
inspectors are paid $12 per hour. Will it be profitable to hire another man-hour of inspection
capacit at a price of 12 dollars? How do you know?

(d) At what price would should be willing to rent 1 machine-hour of vibration to a competing
producer? How many machine-hours can be rented out before your optimal solution changes.

Problem 3 Sensitivity Analysis. A masonry plant produces four types of breeze-blocks type of brick made from concrete rather than clay). There are three stages of the manufacturing process which require labor: Mixing, Vibrating, and Inspection. During the next month, there are 700 machine-hours available for mixing, 1100 machine-hours for vibration, and 340 man-hours for inspection. Each variety of breeze-block has its own set of manufacturing requirements given in Table 1 below. Variety 1 2 Profit ($) 8 1 2 Mixing (Mhrs) Vibrating (Mhrs) 1.5 2 Inspection (Mhrs) 0.5 0.6 Table 1: Required hours of labor for each process per one pallet of each variety of breeze-block. 3654 10 15 1 4 22 2
Transcribed Image Text:Problem 3 Sensitivity Analysis. A masonry plant produces four types of breeze-blocks type of brick made from concrete rather than clay). There are three stages of the manufacturing process which require labor: Mixing, Vibrating, and Inspection. During the next month, there are 700 machine-hours available for mixing, 1100 machine-hours for vibration, and 340 man-hours for inspection. Each variety of breeze-block has its own set of manufacturing requirements given in Table 1 below. Variety 1 2 Profit ($) 8 1 2 Mixing (Mhrs) Vibrating (Mhrs) 1.5 2 Inspection (Mhrs) 0.5 0.6 Table 1: Required hours of labor for each process per one pallet of each variety of breeze-block. 3654 10 15 1 4 22 2
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