# Math 540 Assignment 3

Julia is a senior at Tech, and a small entrepreneur. She wants to lease a food booth outside the Tech stadium for the home football games, so she can make profit to finance a final year. Tech sells out every home game, and the one thing Julia knows from attending the every games, is that everyone eats a lot of food. She has a booth, and the booths are not very large. Vendors can sell either food or drinks on Tech property, but not both. Only the Tech athletic department concession stands can sell both inside the stadium. Then, she had a great idea, she thinks slices of cheese pizza, hot dogs, and barbecue sandwiches are the most popular food items among fans and so these are the items she would sell.

(A)Formulate and solve an L.P. Model for this case.

X1= the number of slices of Pizza; X2 = the number of Hot Dogs; X3 = the number of Sandwiches **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

For Hot Dog = $1.50 – 0.45 = $1.05

For Sandwiches = $2.25 – 0.90 = $1.35

**Maximize**

Z = $0.75(x1) + $1.05(x2) + $1.35(x3)

$0.75(x1) + $0.45(x2) + $0.90(x3) = 2.1

x1,x2,x3 >= 0

**Constraints**

$0.75(x1) + $0.45(x2) + $0.90(x3) =0 (At least twice as many Hot Dogs as BBQ.) x1, x2, x3 >0 (non-negativity constraint) |

Hot Dogs: 1250; BBQ Sandwiches: 0; Pizza: 1250

Amount of Total Food : 1250, +0 +1250

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