2)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:
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.
a. Formulate a linear programming model for this problem.
b. Solve the model by using the computer.
19)As a result of a recently passed bill, a congressman’s district has been allocated $4 million for programs
and projects. It is up to the congressman to decide how to distribute the money. The congressman
has decided 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 0.02
Parks 0.09
Sanitation 0.06
Mobile library 0.04
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 40% 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. The congressman wants to know the amount to allocate to each program
to maximize his votes.
a. Formulate a linear programming model for this problem.
b. Solve the model by using the computer.
20)Anna Broderick is the dietitian for the State University football team, and she is attempting to
determine a nutritious lunch menu for the team. She has set the following nutritional guidelines
for each lunch serving:
Between 1,500 and 2,000 calories
At least 5 mg of iron
At least 20 but no more than 60 g of fat
At least 30 g of protein
At least 40 g of carbohydrates
No more than 30 mg of cholesterol
She selects the menu from seven basic food items, as follows, with the nutritional contribution
per pound and the cost as given:
Calories Iron Protein Carbohydrates Fat Cholesterol
(per lb.) (mg/lb.) (g/lb.) (g/lb.) (g/lb.) (mg/lb.) $/lb.
Chicken 520 4.4 17 0 30 180 0.80
Fish 500 3.3 85 0 5 90 3.70
Ground beef 860 0.3 82 0 75 350 2.30
Dried beans 600 3.4 10 30 3 0 0.90
Lettuce 50 0.5 6 0 0 0 0.75
Potatoes 460 2.2 10 70 0 0 0.40
Milk (2%) 240 0.2 16 22 10 20 0.83
The dietitian wants to select a menu to meet the nutritional guidelines while minimizing the
total cost per serving.
a. Formulate a linear programming model for this problem.
b. Solve the model by using the computer.
c. If a serving of each of the food items (other than milk) was limited to no more than a half
pound, what effect would this have on the solution?
38)Dr. Maureen Becker, the head administrator at Jefferson County Regional Hospital, must determine
a schedule for nurses to make sure there are enough of them on duty throughout the day.
During the day, the demand for nurses varies. Maureen has broken the day into twelve 2-hour
periods. The slowest time of the day encompasses the three periods from 12:00 A.M. to 6:00 A.M.,
which, beginning at midnight, require a minimum of 30, 20, and 40 nurses, respectively. The demand
for nurses steadily increases during the next four daytime periods. Beginning with the
6:00 A.M.–8:00 A.M. period, a minimum of 50, 60, 80, and 80 nurses are required for these four
periods, respectively. After 2:00 P.M. the demand for nurses decreases during the afternoon and
evening hours. For the five 2-hour periods beginning at 2:00 P.M. and ending at midnight, 70, 70,
60, 50, and 50 nurses are required, respectively. A nurse reports for duty at the beginning of one
of the 2-hour periods and works 8 consecutive hours (which is required in the nurses’ contract
Dr. Becker wants to determine a nursing schedule that will meet the hospital’s minimum requirements
throughout the day while using the minimum number of nurses.
a. Formulate a linear programming model for this problem.
b. Solve this model by using the computer.
48)The production manager of Videotechnics Company is attempting to determine the upcoming
5-month production schedule for video recorders. Past production records indicate that 2,000
recorders can be produced per month. An additional 600 recorders can be produced monthly on
an overtime basis. Unit cost is $10 for recorders produced during regular working hours and $15
for those produced on an overtime basis. Contracted sales per month are as follows:
Month Contracted Sales (units)
1 1,200
2 2,100
3 2,400
4 3,000
5 4,000
Inventory carrying costs are $2 per recorder per month. The manager does not want any inventory
carried over past the fifth month. The manager wants to know the monthly production that will
minimize total production and inventory costs.
a. Formulate a linear programming model for this problem.
b. Solve the model by using the computer.
"96% of our customers have reported a 90% and above score. You might want to place an order with us."
