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# Linear programming: Graphical Method, Sensitivity Analysis

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The manager of a Burger Doodle franchise wants to determine how many sausage biscuits and ham biscuits to prepare each morning for breakfast customers. Each type of biscuit requires 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.

On a separate spreadsheet, Solve the linear programming model formulated above graphically.

a) How much extra sausage and ham are 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?