Please provide linear programming model, graphical solution, sensitivity report, and answers to questions A thru C. (Problem on page 2)

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A) Formulate and solve a linear programming model for Julia that will help you advise her if she should lease the booth. Let, X1 =No of pizza slices, X2 =No of hot dogs, X3 = barbeque sandwiches Formulation: 1. Calculating Objective function co-efficients: The objective is to Maximize total profit. Profit is calculated for each variable by subtracting cost from the selling price. • For Pizza slice, Cost/slice=$6/8=$0.75

| |X1 |X2 |X3 |

| SP | $ 1.50 | $ 1.50 | $ 2.25 |

|-Cost | $ 0.75 | $ 0.45 | $ 0.90 |

| | | | |

|Profit | $ 0.75 | $ 1.05 | $ 1.35 |

• Total space available=3*4*16=192 sq feet =192*12*12=27,648 in- square The oven will be refilled during half time. Thus, the total space available=2*27,648= 55,296 in-square • Space required for a pizza=14*14=196 in-square Space required for a slice of pizza=196/8=24 in-square approximately.

Thus, Objective function for the model can be written as: Maximize Total profit Z = $0.75X1 + 1.05X2 +1.35X3 Subject to constraints: $0.75X1 + .0.45X2 + 0.90X3 = 2.0 (at least twice as many hot dogs as barbeque sandwiches) This constraint can be rewritten as: X2-2X3>=0 X1, X2, X3 >= 0

Final Model: Maximize Total profit Z = $0.75X1 + 1.05X2 +1.35X3 Subject to: $0.75X1 + .0.45X2 + 0.90X3 =0 (at least twice as many hot dogs as barbeque sandwiches) X1, X2, X3 >= 0 (Non negativity constraint)