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Date Submitted: 09/09/2012 06:06 PM
Assignment #3: Julia's Food Booth
Hope Whaley
Professor: Dr. Daryl Brydie
Quantitative Methods - MAT 540
August 19, 2012
(A) Formulate and solve an L.P. model for this case.
X1 – Pizza
X2 – Hot Dogs
X3 – Barbecue Sandwiches
Objective: Maximize profits = Profit at least $1,000.00 after each game.
Profit = Sell – Cost
Profit Function: Z = 0.75(X1) + 1.05(X2) + 1.35(X3)
Constraints and Cost:
Maximum fund available for the purchase = $1,500.00
Cost per pizza slice = $0.75 because she purchase each pizza for $6.00 and there are 8
slices per pizza.
Cost per hot dog = $0.45
Cost per sandwich = $0.90
Constraint = 0.75(X1) + 0.45(X2) + 0.90(X3) < 1500
Warming Oven:
Space available: 3 x 4 x 16 = 192 sq feet = 192 x 12 x 12 = 27,648 sq inches
Oven will be filled twice per game: 27,648 x 2 = 55,296
Space required for pizza: 14 x 14 = 196 sq inches
Space required for each pizza slice: 196/8 = 24.5 sq inches
Space required for each hot dog: 16 sq inches
Space required for each sandwich: 25 sq inches
Constraint: 24.5(X1) + 16(X2) + 25(X3) < 55,296
Julia can sell twice as many pizza slices(X1) as hot dogs(X2) and
sandwiches(X3), combined.
X1 > X2 + X3 = X2 – 2(X3) > 0
Julia can sell twice as many hot dogs(X2) as barbecue sandwiches(X3).
X2/X3 > 2 = X2 > 2(X3) = X2 – 2(X3) > 0
X1, X2, X3 >= 0 (Non-negativity constraint)
LPP Model:
Maximize Profit: Z = 0.75(X1) + 1.05(X2) + 1.35(X3)
Subject to 24.5(X1) + 16(X2) + 25(X3) < 55,296
0.75(X1) + 0.45(X2) + 0.90(X3) < 1,500
X1 – X2 – X3 > 0
X2 – 2(X3) > 0
X1 > 0, X2 > 0 and X3 > 0
Food Items: |Pizza |Hot Dogs |Barbecue | | | | | |Profit Per Item: |$0.75 |$1.05 |$1.35 | | | | | | | | | | | | | |...