Max Z =Profit1x1+ Profit2x2+ Profit3x3
A - Formulation of the LP model
x1 - number of pizza slice
x2 - number of hot dogs
x3 - number of barbecue sandwiches
Constraints
Cost
Maximum fund available for food = $1500
Cost per pizza $6 ÷08 (slices) = $0.75
Cost for a hot dog = $0.45
Cost for a barbecue sandwich = $0.90
Constraint: 0.75x1+0.45x2+0.90x3 ≤1500
Oven space
Space available 16.3.4.2 = 384ft^2
384.144=55296 in ^2
Space required for pizza: 14.14 = 196 ^2 inches
Space for slice of pizza; 196 ÷8 = 24.50 in ^2
Space for hot dog: 16 in ^2
Space for barbecue = 25 in ^2
Constraint 24.50x1+16x2+25x3 ≤55296
Julia can sell at least as many slice of pizza (x1) as hot dogs (x2) and Barbecue sandwiches (x3) combined. x1-x2-x3≥0
Julia can sell at least twice as many hot dogs as Barbecue sandwiches +x2-2x3≥0
Non negative constraint
x1,x2,x3≥0
Objective Function
| SELL| COST| PROFIT|
Pizza slice (x1) | $1.50 | $0.75 | $0.75| Hot dog (x2) | $1.50 | $0.45 | $1.05| Barbecue Sandwich (x3) | $2.25 | $0.90 | $1.35| Profit = Sell - Cost

Max Z=0.75x1+1.05x2+1.35x3
LPP Model:
Maximize Z = 0.75 X1 + 1.05 X2 + 1.35 X3
Subject to 24.5 X1 + 16 X2 + 25 X3 ≤ 55296
0.75 X1 + 0.45 X2 + 0.90 X3 ≤ 1500
X1 - X2 - X3 ≥ 0
X2 - 2 X3 ≥ 0
X1≥ 0, X2≥ 0 and X3 ≥0
Solve the LPM -answer in QM for Windows solution
Based on the QM for Windows solution the optimum solution:
Pizza (X1) = 1250; Hotdog s(X2) = 1250 and Barbecue sandwiches (X3) = 0 Optimal solution value Z = $2250
Julia should stock 1250 slices of pizza, 1250 hot dogs and no barbecue sandwiches. Maximum Profit = $2250.
Maximum Profit| $ 2,250.00|
Booth Rent per game| $ (1,000.00)|
Warming Oven 600 for total of 6 home games 600/6 =100| $ (100.00)| Profit for the 1st Game| $ 1,150.00...

...stock 1250 slices of pizza and 1250 numbers of Hot dogs. She need not stock sandwiches.
Maximum Profit that can be expected is $2250.
Lease cost for the booth per game = $1000
Lease cost for the oven per game = $100
Net profit after all the expenses = 2250 – 1100 = $1150
Now it is clear that as per the strategy it is worth leasing the booth.
B) The sensitivity report of the solution is given below
| | | ...

...Julia’sFoodBooth
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 foodbooth 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...

...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 |...

...Complete the "Julia'sFoodBooth" caseproblem on page 109 of the text. Address each of the issues A - D according the instructions given.
(A) Formulate and solve an L.P. model for this case.
(B) Evaluate the prospect of borrowing money before the first game.
(C) Evaluate the prospect of paying a friend $100/game to assist.
(D) Analyze the impact of uncertainties on the model.
The...

...(A) Formulate and solve an L.P. model for this case
Variable Food Cooking Area
x1 Pizza Slice 24in sq
x2 Hot Dogs 16in sq
x3 BBQ Sandwiches 25in sq
*The oven space required for a pizza slice is calculated by dividing the total area arequired for a whole pizza by the number of slices in a pizza 14 x 14 = 196 in2, by 8, or approximately 24 in2 per slice. The total space available is the dimension of a shelf, 36 in. x 48 in. = 1,728 in2, multiplied by 16...

...pizza, 1250 hot dogs and no barbecue sandwiches.
Maximum Profit = $2250.
|Maximum Profit 2250
Booth Rent per game 1000
Warming Oven 600 for total of 6 games 600/6 =100 for 1 game
2250-1000-100=1150 is the profit after paying all the expenses.
*I think she should lease the booth
B) the amount of Borrowing money that will increase her profit is defined by the upper limit...

...Julia’sFoodBooth
Strayer University
Quantitative Methods – MAT 540/ Spring 2012
Dr. Buddy Bruner
May 19, 2012
A) Formulate and solve an L.P. model for this case.
[pic]
[pic]
B) Evaluate the prospect of borrowing money before the first game.
After observing the ranging chart calculations indicate that the upper bound in...