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