Mathematical Modeling Question 1. Tech Covers Inc. Production Planning "Tech Covers Inc." is a company that produces covers for three types of devices: laptops, tablets, and smartphones. The company's production facilities allow them to produce 8000 laptop covers, 5000 tablet covers, or 7000 smartphone covers in one day only if the entire production is devoted to one type of cover (in other words, producing 8000 laptop covers, or 5000 tablet covers, or 7000 smartphone covers takes one full working day). The production schedule is one week (5 working days), and the week's production must be stored before distribution. Storing 1000 laptop covers (packaging included) takes up 60 cubic feet of space, while storing 1000 tablet covers (packaging included) takes up 30 cubic feet of space and storing 1000 smartphone covers (packaging included) takes up 40 cubic feet of space. The total storage space available is 8000 cubic feet. Due to agreements with major electronics retailers, Tech Covers Inc. has to deliver at least 6000 laptop covers and 4000 tablet covers per week to strengthen the product's market presence. The marketing department estimates that the weekly demand for laptop covers, tablet covers, and smartphone covers does not exceed 12000, 10000, and 15000 units, respectively. Therefore, the company does not want to produce more than these amounts for laptop, tablet, and smartphone. covers. Finally, the net profit per each laptop cover, tablet cover, and smartphone cover is $5, $8, and $10, respectively. (a) Write a Linear Programming formulation for the problem. You must label each constraint. (Hint: define decision variables as the number of items of each produced over the week). (b) Solve your developed model using Excel and obtain the optimal weekly production plan of this company.
Mathematical Modeling Question 1. Tech Covers Inc. Production Planning "Tech Covers Inc." is a company that produces covers for three types of devices: laptops, tablets, and smartphones. The company's production facilities allow them to produce 8000 laptop covers, 5000 tablet covers, or 7000 smartphone covers in one day only if the entire production is devoted to one type of cover (in other words, producing 8000 laptop covers, or 5000 tablet covers, or 7000 smartphone covers takes one full working day). The production schedule is one week (5 working days), and the week's production must be stored before distribution. Storing 1000 laptop covers (packaging included) takes up 60 cubic feet of space, while storing 1000 tablet covers (packaging included) takes up 30 cubic feet of space and storing 1000 smartphone covers (packaging included) takes up 40 cubic feet of space. The total storage space available is 8000 cubic feet. Due to agreements with major electronics retailers, Tech Covers Inc. has to deliver at least 6000 laptop covers and 4000 tablet covers per week to strengthen the product's market presence. The marketing department estimates that the weekly demand for laptop covers, tablet covers, and smartphone covers does not exceed 12000, 10000, and 15000 units, respectively. Therefore, the company does not want to produce more than these amounts for laptop, tablet, and smartphone. covers. Finally, the net profit per each laptop cover, tablet cover, and smartphone cover is $5, $8, and $10, respectively. (a) Write a Linear Programming formulation for the problem. You must label each constraint. (Hint: define decision variables as the number of items of each produced over the week). (b) Solve your developed model using Excel and obtain the optimal weekly production plan of this company.
Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter5: Network Models
Section5.5: Shortest Path Models
Problem 32P
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Question 1. Tech Covers Inc. Production Planning
"Tech Covers Inc." is a company that produces covers for three types of devices: laptops, tablets,
and smartphones. The company's production facilities allow them to produce 8000 laptop covers,
5000 tablet covers, or 7000 smartphone covers in one day only if the entire production is
devoted to one type of cover (in other words, producing 8000 laptop covers, or 5000 tablet
covers, or 7000 smartphone covers takes one full working day). The production schedule is one
week (5 working days), and the week's production must be stored before distribution. Storing 1000
laptop covers (packaging included) takes up 60 cubic feet of space, while storing 1000 tablet covers
(packaging included) takes up 30 cubic feet of space and storing 1000 smartphone covers (packaging
included) takes up 40 cubic feet of space. The total storage space available is 8000 cubic feet.
Due to agreements with major electronics retailers, Tech Covers Inc. has to deliver at least
6000 laptop covers and 4000 tablet covers per week to strengthen the product's market presence.
The marketing department estimates that the weekly demand for laptop covers, tablet covers, and
smartphone covers does not exceed 12000, 10000, and 15000 units, respectively. Therefore, the
company does not want to produce more than these amounts for laptop, tablet, and smartphone
covers. Finally, the net profit per each laptop cover, tablet cover, and smartphone cover is $5, $8,
and $10, respectively.
(a) Write a Linear Programming formulation for the problem. You must label each constraint.
(Hint: define decision variables as the number of items of each produced over the week).
(b) Solve your developed model using Excel and obtain the optimal weekly production plan of this
company.
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