X2 = Hot Dogs X3 = BBQ Sandwiches The objective is to maximize profit. maximize Z= 0 .75X1+1.05X2+1.35X3 Subject to: 0.75X1+1.05X2+1.35X3≤1‚500(Budget) 24X1+16X2+25X3≤55‚296in2 (Oven space) X1≥X2+X3 X2X3≥2.0 X1‚ X2‚ X3≥0 Julia’s Food Booth Food items: Pizza Hot Dogs Barbecue Profit per item: 0.75 1.05 1.35 Constraints: Available Usage Left over Budget ($) 0.75 0.45 0.90 1‚500 1‚500.00 0 Oven space (sq. in.) 24 16 25 55‚296 50‚000.00 5296 Demand
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Julia Food Booth Introduction Julia is planning to lease a food booth outside the Tech Stadium at Home Football games to finance her last year education with all the games go sold out. The rent for the booth per game is $ 1000. Julia will sell slices of Cheese Pizza‚ Hot Dogs and Barbecue Sandwiches which are acclaimed to be the most popular so these are the three products she has chosen to sell at the home games football stadium. The rent for oven is $ 600 for six home games‚ which
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Julia’s Food Booth (A) Formulate and solve an LP model for this case The objective here is to maximize the profit. Profit is calculated for each variable by subtracting cost from the selling price. The decision variables used are X1 for pizza slices‚ X2 for hotdog‚ and X3 for BBQ sandwich. X1 (pizza) X2 (hotdog) X3 (sandwich) Sales Price 1.50 1.50 2.25 Cost 0.75 0.45 0.90 Profit 0.75 1.05 1.35 *For Pizza Slice: Cost/Slice = $6/8 = $0.75 cost per slice Maximize Z =
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a) P=PIZZA H=HOTDOGS S=BARBEQUE SANDWHICHES The L.P. for this case is‚ Maximize: P= 0.75P +1.05H +1.35S Subject to: 24.5p +16h +25s ≤ 55296 0.75p + 0.45h+0.90s ≤ 1500 P – h – s ≥ 0 H - 2s ≥ 0 P ‚ h ‚ s ≥ 0 The optimal solution occurs when P=1250 h-1250 s=0 Profit =$2250 Since the booth costs $1000 to lease per game‚ and the oven is $100 per game‚ then Julia’s overall profit is‚ P = 2250 - 1100 = $1150 Hence it is worth leasing the booth. b) The shadow price for
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Julia Booth Case Study Angela Walker June‚ 06‚ 2013 Dr. Carl Tucker field In this case study‚ I must create a linear programming model for Julia that will help her to decide whether or not she need to lease a booth. The three products or variable we must consider for this booth are pizza‚ hotdogs‚ and barbecue sandwiches. In this model‚ x 1 equal the number of pizza slices Julia should purchase‚ x2 equals the number of hotdogs Julia should purchase‚ and x3 equal the number of barbecue sandwiches
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Assignment #3: JULIA`S FOOD BOOTH A. Julia would make $1150 profit after paying all expenses after the first game. And then she would make $1721.22 for the rest of the games. Since she will be clearing her number of $1000 profit per game‚ she should lease the booth. B. If she borrows money from a friend she would increase her profit. She would borrow $380.82 from a friend and she will make $571.22 more profit. The factor that constraints her from borrowing even more money is the total
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Julia’s Food Booth. Parts A thru C. Please provide linear programming model‚ graphical solution‚ sensitivity report‚ and answers to questions A thru C. (Problem on page 2) [pic] [pic] A) Formulate and solve a linear programming model for Julia that will help you advise her if she should lease the booth. Let‚ X1 =No of pizza slices‚ X2 =No of hot dogs‚ X3 = barbeque sandwiches Formulation: 1. Calculating Objective function co-efficients:
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Julia’s Food Booth Julia Robertson is a senior at Tech‚ and she’s investigating different ways to finance her final year at school. She is considering leasing a food booth outside the Tech stadium at home football games. Tech sells out every home game‚ and Julia knows‚ from attending the games herself‚ that everyone eats a lot of food. She has to pay $1‚000 per game for 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
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A. Formulate a linear programming model for Julia that will help you to advise her if she should lease the booth. Let‚ X1 =No. of pizza slices‚ X2 =No. of hot dogs‚ X3 = No. of barbeque sandwiches * Objective function co-efficient: 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=$4.5/6=$0.75 | X1 | X2 | X3 | SP | $1.50 | $1.60 | $2.25 | -Cost | 0.75 | $0.50 | $1.00 |
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Sandwiches p‚H‚B >= 0 . si>= 0 Based on QM for windows l solution the optimum solution: Pizza (p) = 1250; Hotdogs(H) = 1250 and Barbecue sandwiches (B) = 0 Maximum value of Z = $2250 Julia should stock 1250 slices of pizza‚ 1250 hot dogs and no barbecue sandwiches. Maximum Profit = $2250. |Maximum Profit
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