Julia S Food Booth
Assignment #3
The following variables will be used:
X1 = Slices of Pizza
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
1
-1
-1
0 -
0
Demand
0
1
-2
0
1,250.00 -1250
Stock
Pizza=
1250
slices
Hot Dogs=
1250
hot dogs
Barbecue=
0
sandwiches
Profit=
2,250.00
Sensitivity Report
Adjustable Cells
Final
Reduced
Objective
Allowable
Allowable
Cell
Name
Value
Cost
Coefficient
Increase
Decrease
$B$12
Pizza=
1250
0
0.75
1
1.00
$B$13
Hot Dogs=
1250
0
1.05
1E+30
0.27
$B$14
Barbecue=
0
0
1.35
0.375000011
1E+30
Constraints
Final
Shadow
Constraint
Allowable
Allowable
Cell
Name
Value
Price
R.H. Side
Increase
Decrease
$G$9
Demand Usage
1,250.00
-
0
1250
1E+30
$G$7
Oven space (sq. in.) Usage
50,000.00
-
55296
1E+30
5296
$G$6
Budget ($) Usage
1,500.00
1.50
1500
158.88
1500
$G$8
Demand Usage - (0.38)
0
2000
3333.33
I believe that Julia would increase her profit if she borrowed some more money from a friend. Her shadow price, or dual value, is $1.50 for each additional dollar that she earns. The upper limit given in the model is $1,658.88, which means that Julia can borrow only $158.88 from her friend, which would give her an additional profit of $238.32.
Evaluate the prospect of paying a friend $100/game to assist.
In order for Julia to be able to prepare the BBQ sandwiches and hot dogs in a short period of time to make her profit, she needs the additional help. With her borrowing
The following variables will be used:
X1 = Slices of Pizza
X2 = Hot Dogs
X3 = BBQ Sandwiches
The objective is to maximize profit. maximize Z= 0 .75X1+1.05X2+1.35X3
Subject to:
0.75X1+1.05X2+1.35X3≤1,500(Budget)
24X1+16X2+25X3≤55,296in2 (Oven space)
X1≥X2+X3
X2X3≥2.0
X1, X2, X3≥0
Julia’s Food Booth
Food items: Pizza
Hot Dogs
Barbecue
Profit per item:
0.75
1.05
1.35
Constraints:
Available
Usage
Left over
Budget ($)
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
1
-1
-1
0 -
0
Demand
0
1
-2
0
1,250.00 -1250
Stock
Pizza=
1250
slices
Hot Dogs=
1250
hot dogs
Barbecue=
0
sandwiches
Profit=
2,250.00
Sensitivity Report
Adjustable Cells
Final
Reduced
Objective
Allowable
Allowable
Cell
Name
Value
Cost
Coefficient
Increase
Decrease
$B$12
Pizza=
1250
0
0.75
1
1.00
$B$13
Hot Dogs=
1250
0
1.05
1E+30
0.27
$B$14
Barbecue=
0
0
1.35
0.375000011
1E+30
Constraints
Final
Shadow
Constraint
Allowable
Allowable
Cell
Name
Value
Price
R.H. Side
Increase
Decrease
$G$9
Demand Usage
1,250.00
-
0
1250
1E+30
$G$7
Oven space (sq. in.) Usage
50,000.00
-
55296
1E+30
5296
$G$6
Budget ($) Usage
1,500.00
1.50
1500
158.88
1500
$G$8
Demand Usage - (0.38)
0
2000
3333.33
I believe that Julia would increase her profit if she borrowed some more money from a friend. Her shadow price, or dual value, is $1.50 for each additional dollar that she earns. The upper limit given in the model is $1,658.88, which means that Julia can borrow only $158.88 from her friend, which would give her an additional profit of $238.32.
Evaluate the prospect of paying a friend $100/game to assist.
In order for Julia to be able to prepare the BBQ sandwiches and hot dogs in a short period of time to make her profit, she needs the additional help. With her borrowing