Mill
Aluminum
Grade
1
2
High
6
2
Medium
2
2
Low
4
10
The company has contracted with a manufacturing firm to supply at least 12 tons of high-grade aluminum, 8 tons of medium-grade aluminum, and 5 tons of low grade aluminum. It costs United $6000 per day to operate mill 1 and $7000 per day to operate mill 2. The company wants to know the number of days to operate each mill in order to meet the contract at the minimum cost.
Formulate a linear programming model for this problem.
16. Solve the linear programming model formulated in Problem 14 for United Aluminum Company by using the computer.
a. Identify and explain the shadow prices for each of the aluminum grade contract requirements.
b. Identify the sensitivity ranges for the objective function coefficients and the constraint quantity values.
c. Would the solution values change if the contract requirements for high-grade aluminum were increased for 12 tons to 20 tons? If yes what would the new solutions values be?
22. Solve the linear programming model developed below for the Burger Doodle restaurant by using the computer.
Biscuit
Labor (hr)
Sausage (lb)
Ham (lb)
Flour (lb)
Sausage
0.01
0.1
-
0.04
Ham
0.024
-
0.15
0.04
a. Identify and explain the shadow prices for each of the resource constraints.
b. Which of the resources constraints profit the most?
c. Identify the sensitivity ranges for the profit of a sausage biscuit and the amount of sausage available. Explain these sensitivity ranges.
