Problem:
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 know the number of each type of biscuit to prepare each morning in order to maximize profit.
Formulate a linear programming model for this problem.
Solve the linear programming model developed for the Burger Doodle restaurant by using the computer.
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.