12.3-4. The Toys-R-4-U Company has developed two new toys for possible inclusion in its product line for the upcoming Christmas season. Setting up the production facilities to begin production would cost $50,000 for toy 1 and $80,000 for toy 2. Once these costs are covered, the toys would generate a unit profit of $10 for toy 1 and $15 for toy 2. The company has two factories that are capable of producing these toys. However, to avoid doubling the start-up costs, just one factory would be used, where the choice would be based on max- imizing profit. For administrative reasons, the same factory would be used for both new toys if both are produced. Toy 1 can be produced at the rate of 50 per hour in factory 1 and 40 per hour in factory 2. Toy 2 can be produced at the rate of 40 per hour in factory 1 and 25 per hour in factory 2. Factories 1 and 2, respectively, have 500 hours and 700 hours of production time available before Christmas that could be used to produce these toys. It is not known whether these two toys would be continued after Christmas. Therefore, the problem is to determine how many units (if any) of each new toy should be produced before Christ- mas to maximize the total profit. (a) Formulate an MIP model for this problem. (b) Use the computer to solve this model.
12.3-4. The Toys-R-4-U Company has developed two new toys for possible inclusion in its product line for the upcoming Christmas season. Setting up the production facilities to begin production would cost $50,000 for toy 1 and $80,000 for toy 2. Once these costs are covered, the toys would generate a unit profit of $10 for toy 1 and $15 for toy 2. The company has two factories that are capable of producing these toys. However, to avoid doubling the start-up costs, just one factory would be used, where the choice would be based on max- imizing profit. For administrative reasons, the same factory would be used for both new toys if both are produced. Toy 1 can be produced at the rate of 50 per hour in factory 1 and 40 per hour in factory 2. Toy 2 can be produced at the rate of 40 per hour in factory 1 and 25 per hour in factory 2. Factories 1 and 2, respectively, have 500 hours and 700 hours of production time available before Christmas that could be used to produce these toys. It is not known whether these two toys would be continued after Christmas. Therefore, the problem is to determine how many units (if any) of each new toy should be produced before Christ- mas to maximize the total profit. (a) Formulate an MIP model for this problem. (b) Use the computer to solve this model.
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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Transcribed Image Text:12.3-4. The Toys-R-4-U Company has developed two new toys for
possible inclusion in its product line for the upcoming Christmas
season. Setting up the production facilities to begin production
would cost $50,000 for toy 1 and $80,000 for toy 2. Once these
costs are covered, the toys would generate a unit profit of $10 for
toy 1 and $15 for toy 2.
The company has two factories that are capable of producing
these toys. However, to avoid doubling the start-up costs, just one
factory would be used, where the choice would be based on max-
imizing profit. For administrative reasons, the same factory would
be used for both new toys if both are produced.
Toy 1 can be produced at the rate of 50 per hour in factory 1
and 40 per hour in factory 2. Toy 2 can be produced at the rate of
40 per hour in factory 1 and 25 per hour in factory 2. Factories
1 and 2, respectively, have 500 hours and 700 hours of production
time available before Christmas that could be used to produce
these toys.
It is not known whether these two toys would be continued
after Christmas. Therefore, the problem is to determine how many
units (if any) of each new toy should be produced before Christ-
mas to maximize the total profit.
(a) Formulate an MIP model for this problem.
(b) Use the computer to solve this model.
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