# Julia's Food Booth

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Running Head: JULIA’S FOOD BOOTH 1 Julia’s Food Booth MAT 540- Quantitative Methods May 30, 2014 JULIA’S FOOD BOOTH 2 A. Formulate and solve a linear programming model for Julia that will help to advise if she should lease the booth. This problem includes three decision variables that represent what Julia is going to sell in her concession booth. * X1= Pizza slices * X2= Hot dogs * X3= Barbeque sandwiches The objective function is to determine how much money Julia is going to make during the first game (maximize profit) and if it is over \$1000 that it will be worth her time to open up the concession booth. Profit is calculated for each variable by subtracting the cost from the selling price. The profits for the variables are calculated in this method: * Pizza slices- Cost per slice = \$6/8= \$.75 per slice so the profit is calculated \$1.50 (selling price) -\$.75 (cost) = \$.75 profit. * Hot dogs- \$1.50 (selling price) - \$.45 (cost) = \$1.05 profit. * Barbeque Sandwiches- \$2.25 (selling price) - \$.90 (cost) = \$1.35 profit. Total profit, which is defined by as “Z”, can be expressed as Z= \$0.75x1 + \$1.05x2 + \$1.35x3 Constraints The first constraint is the total space available in the oven if it has 16 shelves and each shelf is three feet by four feet and one foot equals to 12 inches. The total space of the oven with 16 JULIA’S FOOD BOOTH 3 shelves is calculated 3 x 4 x 16= 192 square feet which then is calculated 192 x 12 x 12