Teneika Smith
Strayer University
Professor Guo
Julia’s Food Booth Assignement #3
A. Formulate and solve an L.P. model for this case.
x1=slices of pizza
x2= Hot Dogs
x3= Barbecue Sandwiches
Maximize, Z= $0.75×1+ $1.05×2+$1.35×3
Constraints:
$0.75×1+$0.45×2+$0.90×3 < = $1500 (cost)
24×1+16×2+25×3< = 55,296 square inches (Oven Space)
***14 x 14 = 196 inches squared 196/8= 24.5. The total space available is 36 in. x 48 in. = 1,728 inches squared Then 1728 is multiplied by 16= 27,648 in2, which is multiplied by 2 totaling 55, 296 square inches***
x1-x2-x3 > = 0 (at least as many slices of pizza as hot dogs and barbecue sandwiches) x2-2×3> = 0 (at least twice as many hot dogs as barbecue sandwiches Non negative constraints
x1, x2, x3 are all > = 0
x1= $1250
x2=$1250
x3=$ 0
Julia’s profit for the first game should be $2, 250. The prices of the booth lease is $1000 per game and the oven lease is $600 for the six game season therefore the lease for the oven is $100 per game decreasing her first game profit to $1150. B. Evaluate the prospect of borrowing money before the first game. Based on the results of the linear programming model in QM the dual value is $1.50. “The dual value measures the increase in the objective function’s value per unit increase in the variable’s value” (Frontline Solvers, 2012).
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Borrowing money before the first game would increase Julia’s profit. The dual value is $1.50 for every additional dollar. C. Evaluate the prospect of paying a friend $100 per game to assist Julia would benefit from hiring an additional friend to assist her because having another person will allow her to make more money because she could more than likely make all the food required to reach maximum profit. D. Analyze the impact of uncertainties on the model.
There are a couple of factors that come to mind when thing about what could affect the sales. For example, the weather could create a problem for Julia if it is raining then it would probably decrease the turn out at the game. There is also the factor of demand if there are not many people who want pizza or hot dogs or barbecue then her profit will be changed.
Reference
Frontline Solvers. Basic Solver-Interpreting the Sensitivity Report. Retrieved from: http://www.solver.com/content/basic-solver-interpreting-sensitivity-report
