1. In The Name Of Allah
Lab 07
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2. LP and Solver
Lab#4
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3. Using Excel’s Solver to solve LP problems
Lab Objectives
Using Excel’s Solver to solve LP problems
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4. Problem 2 ( Exercise )
How many pounds of oat and corn should be fed to each cattle per day to minimize feed cost ?
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5. 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
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6. Step 1 3)- Constraints: 100 X1 + 100 X2 >= 4000
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7. Step 2
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8. Step 3
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9. 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?
Ingredients مقوماات
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10. 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
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11. 3)-Constraints:
X + Y <= 10 X + Y <= 7 200X Y <= 1200 X + 2Y <= 12 X>=0 , Y >=0
area
Cost
Time
Non Negative Value
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12. 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?
Ingredients مقوماات
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13. Profit max = 2x + 3y 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
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14. 3. Express the constraints After getting the unknowns and the objective out of the way, everything else in the problem is a constraint. The constraints are the
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15. X + Y >= 3 20X + 10 Y <= 80 Y <= 2X X , Y >= 0 Processing
Cost
federal regulations
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16. 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.
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17. 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.
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18. 1. Define your unknowns X1 be the number of regular pizza X2 be the number of deluxe pizza
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19. 2. Express the objective Maximize X1 + 1. 5 X2 3
2. Express the objective Maximize X X2 3. Express the constraints Subject to: X1 + X2 <=150 (dough mix ) 0.25 X X2 <= 50 (Topping mix ) X1 >= 50 X2 >= 25 X1 >=0, X2 >= 0
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20. Any Question
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