In The Name Of Allah Lab 07

1. In The Name Of Allah Lab 07

2. LP and Solver Lab#4

3. Lab Objectives • Using Excel’s Solver to solve LP problems

4. Problem 2( Exercise ) How many pounds of oat and corn should be fed to each cattle per day to minimize feed cost ?

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

6. Step 1 3)- Constraints: 100 X1 + 100 X2 >= 4000 200 X1 + 400 X2 >= 10000 200 X1 + 100 X2 >= 5000 X1, X2 >= 0

7. Step 2

8. Step 3

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?

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

11. 3)-Constraints: X + Y <= 10 X + Y <= 7 200X + 100 Y <= 1200 X + 2Y <= 12 X>=0 , Y >=0 area Cost Time Non Negative Value

12. Problem 3 • A gold processor has two sources of gold ore, source A and sourceB. • 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 Bcannot exceed twice the amount of ore from source A. • If ore from sourceA 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?

13. 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

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

15. X + Y >= 3 20X + 10 Y <= 80 Y <= 2X X , Y >= 0 Processing Cost federal regulations

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 least50regular pizzas and at least 25 deluxe pizzas.

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.

18. 1. Define your unknowns X1 be the number of regular pizza X2 be the number of deluxe pizza

19. 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 >= 50X2 >= 25X1 >=0, X2 >= 0

20. Any Question