Case Assignment: Julia's Food Booth

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  • Topic: Food, Weather, Square inch
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MAT 540
Case Assignment #3
Julia’s Food Booth

A. Formulate and solve a linear programming model for Julia that will help you advice her if she should lease the booth.

JULIA’S PRODUCTSTORAGE
VARIABLESCOST SELLING PRICE NEEDED PizzaX1$1.33$1.5014 inches
Hot DogsX2$0.45$1.5016 square inches
BarbecueX3$0.90$2.2525 square inches

Maximize Z= $0.75x1, 1.05x2, 1.35x3

$0.75x1 + .0.45x2 + 0.90x3 = 1,500
24x1 + 16x2 + 25x3 < 55,296 in2 of oven space.
x1 > x2 + x3
>2.0
x1, x2, x3 > 0

(A) Solution: x1 = 1,250 pizza slices
x2= 1,250 hot dogs
x3= 0 barbecue sandwiches
Z= $2,250

B. If Julia were to borrow some more money from a friend before the first game to purchase more ingredients, could she increase her profit? If so, how much should she borrow and how much additional profit would she make? What factor constrains her from borrowing even more money than this amount (indicated in your answer to the previous question?)

|  |Final |Reduced |Objective |Allowable |Allowable | |Name |Value |Cost |Coefficient |Increase |Decrease | |X1 |1250.00 |0.00 |0.75 |1 |1.00000001 | |X2 |1250.00 |0.00 |1.05 |1E+30 |0.272727279 | |X3 |0.00 |-0.38 |1.350000002 |0.375000011 |1E+30 | |  |  |  |  |  |  | |  |  |  |  |  |  | |  |Final |Shadow |Constraint |Allowable |Allowable | |Name |Value...
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