UFESI6314b20329e767fc801a117717a3119d04f26ea48ddf.xls Problem Statementpage 1 of 9
Luther Setzer
1 NASA Pkwy E Stop NEM3, Kennedy Space Center, FL 32899 (321) 5447435
Food
Price
Pizza
1
1
3
$10.00
Cheese Sticks
2
0
1
$6.00
Calzones
2
1
1
$8.00
(dough)
(sauce)
(cheese)
Another DMOR Sensitivity Analysis Example
10/02/07
My family owns an Italian restaurant, even though they only know
how to make three Italian dishes:
pizza, cheese sticks, and
calzones.
They would like to determine how much of each food
product to make.
Each food consists of dough, sauce, and cheese.
We have 20 units
of dough, 10 units of sauce, and 40 units of cheese available to
us.
Consider the following grid of resource utilization by each
food, and price for which they can sell the food.
Dough
Consumption
Sauce
Consumption
Cheese
Consumption
We can thus model this problem as the following linear program,
where
x
1
is the amount of pizza produced,
x
2
is the amount of cheese
sticks produced, and
x
3
is the amount of calzones produced:
Maximize
z
= 10
x
1
+ 6
x
2
+ 8
x
3
subject to
x
1
+ 2x
2
+ 2
x
3
≤
20
x
1
+
x
3
≤ 10
3
x
1
+
x
2
+
x
3
≤ 40
x
≥
0
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UFESI6314
b20329e767fc801a117717a3119d04f26ea48ddf.xls Standard Form
page 2 of 9
Luther Setzer
1 NASA Pkwy E Stop NEM3, Kennedy Space Center, FL 32899 (321) 5447435
Begin by recasting these equations into standard form.
maximize:
subject to:
After optimizing this problem, we have the following optimal simplex tableau.
Basics
z
RHS
z
1.0
0.0
0.0
5.0
3.0
7.0
0.0
130.0
0.0
0.0
1.0
0.5
0.5
0.5
0.0
5.0
0.0
1.0
0.0
1.0
0.0
1.0
0.0
10.0
0.0
0.0
0.0
2.5
0.5
2.5
1.0
5.0
Check the optimal tableau using standard simplex tool.
Maximize z = 10x1+6x2+8x3 subject to
x1+2x2+2x3 <= 20
x1+x3 <= 10
3x1+x2+x3 <= 40
Optimal Solution: z = 130; x1 = 10, x2 = 5, x3 = 0
01
z
 10
x
1
 06
x
2
 08
x
3
= 0.00
00
z
+ 01
x
1
+ 02x
2
+ 02
x
3
+ 01
s
1
+ 00
s
2
+ 00
s
3
= 20
00z + 01
x
1
+ 00
x
2
+ 01
x
3
+ 00
s
1
+ 01
s
2
+ 00
s
3
= 10
00z + 03
x
1
+ 01
x
2
+ 01
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 Fall '09
 VLADIMIRLBOGINSKI
 Kennedy Space Center, Luther Setzer

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