Transcript الشريحة 1

In The Name Of Allah
Lab 07
ins. Tahani Aldweesh
LP and Solver
Lab#4
ins. Tahani Aldweesh
Lab Objectives
 Using
Excel’s Solver to solve LP
problems
ins. Tahani Aldweesh
Problem 2 ( Exercise )
How many pounds of oat and corn should be fed to
each cattle per day to minimize feed cost ?
ins. Tahani Aldweesh
Step 1
1)-Decision variables:
-Let X1 be the pounds of oat to be used .
-Let X2 be the pounds of corn to be used
2)-Objective Function:
Minimize 5 * X1 + 3 * X2
ins. Tahani Aldweesh
Step 1
3)- Constraints:
100 X1 + 100 X2 >= 4000
200 X1 + 400 X2 >= 10000
200 X1 + 100 X2 >= 5000
X1, X2 >= 0
ins. Tahani Aldweesh
Step 2
ins. Tahani Aldweesh
Step 3
ins. Tahani Aldweesh
Problem 2
A farmer has 10 acres to plant in wheat and rye.
 He has to plant at least 7 acres.
 he has only $1200 to spend and each acre of wheat costs
$200 to plant and each acre of rye costs $100 to plant.

the farmer has to get the planting done in 12 hours and it
takes an hour to plant an acre of wheat and 2 hours to
plant an acre of rye.
If the profit is $500 per acre of wheat and $300 per acre of
rye
how many acres of each should be planted to maximize
profits?
ins. Tahani Aldweesh
Step 1
1)-Decision variables:
Let x = the number of acres of wheat
and y = the number of acres of rye.
2)-Objective Function:
Profit max= 500x + 300y
ins. Tahani Aldweesh
3)-Constraints:
X + Y <= 10
X + Y <= 7
area
200X + 100 Y <= 1200
Cost
X + 2Y <= 12
Time
X>=0 ,Y >=0
Non Negative Value
ins. Tahani Aldweesh
Problem 3
A gold processor has two sources of gold ore, source A and
source B.
 In order to keep his plant running, at least three tons of ore must
be processed each day.
 Ore from source A costs $20 per ton to process, and ore from
source B costs $10 per ton to process.
 Costs must be kept to less than $80 per day.
 Moreover, Federal Regulations require that the amount of ore
from source B cannot exceed twice the amount of ore from
source A.
 If ore from source A yields 2 oz. of gold per ton, and ore from
source B yields 3 oz. of gold per ton .
how many tons of ore from both sources must be processed each
day to maximize the amount of gold extracted subject to the
above constraints?

ins. Tahani Aldweesh
1. Define the unknowns
Let x = the number of tons from source A
and y = the number of tons from source B
2. Express the objective
The objective is to maximize the amount of
the gold yield. Since each ton of ore from
source A yields 2oz. of gold and each ton of
ore from source B yields 3oz. of gold, the
amount of gold recovered will be
Profit max = 2x + 3y
ins. Tahani Aldweesh
3. Express the constraints
After getting the unknowns and the
objective out of the way, everything else
is a constraint. The in the problem
constraints are the
ins. Tahani Aldweesh
X + Y >= 3
Processing
Cost
20X + 10 Y <= 80
Y <= 2X
federal regulations
X ,Y >= 0
ins. Tahani Aldweesh
Problem 4






Bryant's Pizza, Inc. is a producer of frozen pizza
products.
The company makes a net income of $1.00 for each
regular pizza and $1.50 for each deluxe pizza produced.
The firm currently has 150 pounds of dough mix and
50 pounds of topping mix.
Each regular pizza uses 1 pound of dough mix and 4
ounces (16 ounces= 1 pound) of topping mix.
Each deluxe pizza uses 1 pound of dough mix and 8
ounces of topping mix.
Based on the past demand per week, Bryant can sell at
least 50 regular pizzas and at least 25 deluxe pizzas.
ins. Tahani Aldweesh

The problem is to determine the number
of regular and deluxe pizzas the company
should make to maximize net income.
Formulate this problem as an LP problem.
ins. Tahani Aldweesh
1. Define your unknowns
X1 be the number of regular pizza
X2 be the number of deluxe
pizza
ins. Tahani Aldweesh
2. Express the objective
Maximize X1 + 1.5 X2
3. Express the constraints
Subject to:
X1 + X2 <=150 (dough mix )
0.25 X1 + 0.5 X2 <= 50 (Topping mix )
X1 >= 50
X2 >= 25
X1 >=0, X2 >= 0
ins. Tahani Aldweesh
Any Question
ins. Tahani Aldweesh