Linear Programming Model

14.
United Aluminum Company of Cincinnati produces three grades (high, medium, and low) of aluminum at two mills. Each mill has a different production capacity (in tons per day) for each grade as follows:

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 aluminum tons of medium-grade aluminum, and 5 tons of low grade aluminum. Its cost 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 program.

16.
Solve the linear programming model formulated in Problem 14 for United Aluminum Company by using the computer.

A. Identify and explain the shadows 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 from 12 tons to 20 tons? If yes, what would the new solution value be?

20.
The manager of a Burger Doodle franchise wants to determine how many sausage biscuits and ham biscuits to prepare each morning for breakfast customers. The two types of biscuits require the following resources:

Biscuit Labor(hr.) Sausage (lb.) Ham (lb.) Flour (lb.)
Sausage 0.010 0.10 ---- 0.04
Ham 0.024 --- 0.15 0.04

The franchise has 6 hours of labor available each morning. The manager has a contract with a local grocer for 30 pounds of sausage and 30 pounds of ham each morning. The manager also purchases 16 pounds of flour. The profit for a sausage biscuit is $0.60; the profit for a ham biscuit is $0.50. The manager wants to knows the number each type of biscuit to prepare each morning in order to maximize profit.

Formulate a linear programming model for this problem.

21.
Solve the linear programming model formulated in Program 20 for the Burger Doodle restaurant graphically.

A. How much extra sausage and ham is left over at the optimal solution point? Is there any idle labor time?
B. What would the solution be if the profit for a ham biscuit were increased from $0.50 to $0.60?
C. What would be the effect on the optimal solution if the manager could obtain 2 more pounds of flour?