MAT 540 Week 8 Chapter 4 Homework

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Chapter 4

1. Betty Malloy, owner of the Eagle Tavern in Pittsburgh, is preparing for Super Bowl Sunday, and she must determine how much beer to stock. Betty stocks three brands of beer- Yodel, Shotz, and Rainwater. The cost per gallon (to the tavern owner) of each brand is as follows:

 Brand Cost/Gallon Yodel \$1.50 Shotz Rainwater

The tavern has a budget of \$2,000 for beer for Super Bowl Sunday. Betty sells Yodel at a rate of \$3.00 per gallon, Shotz at \$2.50 per gallon, and Rainwater at \$1.75 per gallon. Based on past football games, Betty has determined the maximum customer demand to be 400 gallons of Yodel, 500 gallons of shotz, and 300 gallons of Rainwater. The tavern has the capacity to stock 1,000 gallons of beer; Betty wants to stock up completely. Betty wants to determine the number of gallons of each brand of beer to order so as to maximize profit.

1. Formulate a linear programming model for this problem.
2. Solve the model by using the computer.

1. As result of a recently passed bill, a congressman’s district has been allocated \$3 million for programs and projects. It is up to the congressman to decide how to distribute the money. The congressman has decide to allocate the money to four ongoing programs because of their importance to his district- a job training program, a parks project, a sanitation project, and a mobile library. However, the congressman wants to distribute the money in a manner that will please the most voters, or, in other words, gain him the most votes in the upcoming election. His staff’s estimates of the number of votes gained per dollar spent for the various programs are as follows.

 Program Votes/Dollar Job training Parks Sanitation Mobile library

In order also to satisfy several local influential citizens who financed his election, he is obligated to observe the following guidelines:

• None of the programs can receive more than 30% of the total allocation
• The amount allocated to parks cannot exceed the total allocated to both the sanitation project and the mobile library.
• The amount allocated to job training must at least equal the amount spent on the sanitation project.

Any money not spent in the district will be returned to the government; therefore, the congressman wants to spend it all. Thee congressman wants to know the amount to allocate to each program to maximize his votes.

1. Formulate a linear programming model for this problem.
2. Solve the model by using the computer.

Question Continued in solution

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