Consider the production scheduling problem of the perfume Polly named after a famous celebrity. The manufacturer of the perfume must plan production for the first four months of the year and anticipates a demand of 4000, 5000, 6000, and 4500 gallons in January, February, March, and April, respectively. At the beginning of the year the company has an inventory of 2000 gallons. The company is planning on issuing a new and improved perfume called Pollygone in May, so that all Polly produced must be sold by the end of April. Assume 1

College Algebra (MindTap Course List)
12th Edition
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:R. David Gustafson, Jeff Hughes
Chapter6: Linear Systems
Section6.8: Linear Programming
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Consider the production scheduling problem of the perfume Polly named after a famous
celebrity. The manufacturer of the perfume must plan production for the first four months
of the year and anticipates a demand of 4000, 5000, 6000, and 4500 gallons in January,
February, March, and April, respectively. At the beginning of the year the company has an
inventory of 2000 gallons. The company is planning on issuing a new and improved perfume
called Pollygone in May, so that all Polly produced must be sold by the end of April. Assume
1
that the production cost for January and February is $5 per gallon and this will rise to $5.5
per gallon in March and April. The company can hold any amount produced in a certain
month over to the next month at an inventory cost of $1 per unit.
Question: Formulate a linear optimization model that will minimize the costs incurred
in meeting the demand for Polly in the period January through April. Assume for simplicity
that any amount produced in a given month may be used to fulfill demand for that month.
Transcribed Image Text:Consider the production scheduling problem of the perfume Polly named after a famous celebrity. The manufacturer of the perfume must plan production for the first four months of the year and anticipates a demand of 4000, 5000, 6000, and 4500 gallons in January, February, March, and April, respectively. At the beginning of the year the company has an inventory of 2000 gallons. The company is planning on issuing a new and improved perfume called Pollygone in May, so that all Polly produced must be sold by the end of April. Assume 1 that the production cost for January and February is $5 per gallon and this will rise to $5.5 per gallon in March and April. The company can hold any amount produced in a certain month over to the next month at an inventory cost of $1 per unit. Question: Formulate a linear optimization model that will minimize the costs incurred in meeting the demand for Polly in the period January through April. Assume for simplicity that any amount produced in a given month may be used to fulfill demand for that month.
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ISBN:
9781305652231
Author:
R. David Gustafson, Jeff Hughes
Publisher:
Cengage Learning