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A dog owner wants to minimize the cost of buying dog food for his bullmastiffs. Two types of dog



food are available mixed with three kinds of minerals: calcium, phosphorous, and potassium. The per



kilo cost of dog food A and dog food B are P 20.00 and P 16.00, respectively, whereas the minimum



requirement of calcium, phosphorous and potassium are 75, 50, and 30 units, respectively. Also, in



one kilogram of dog food A, 5 units of calcium, 2 units of phosphorous, and 3 units of potassium are



mixed. Again, in one kilogram of dog food B, 4, 6, 3 units of calcium, phosphorous, and potassium,



respectively are mixed. How many of each type of dog food must be bought to minimize the cost?

A dog owner wants to minimize the cost of buying dog food for his bullmastiffs. Two types of dog

food are available mixed with three kinds of minerals: calcium, phosphorous, and potassium. The per

kilo cost of dog food A and dog food B are P 20.00 and P 16.00, respectively, whereas the minimum

requirement of calcium, phosphorous and potassium are 75, 50, and 30 units, respectively. Also, in

one kilogram of dog food A, 5 units of calcium, 2 units of phosphorous, and 3 units of potassium are

mixed. Again, in one kilogram of dog food B, 4, 6, 3 units of calcium, phosphorous, and potassium,

respectively are mixed. How many of each type of dog food must be bought to minimize the cost?



A farmer can plant up to eight hectares of land with rice and corn. He can earn P 5,000.00 for


every hectare he plants with rice, and P 3,000.00 for every hectare he plants with corn. His use of a


necessary fertilizer is limited by the Credit Cooperative Policy of 10 gallons for his entire 8-hectare


land. Rice requires 2 gallons of fertilizer for every hectare planted, and corn just 1 gallon per hectare.


Find the farmer’s maximum profit

A dog owner wants to minimize the cost of buying dog food for his bullmastiffs. Two types of dog




food are available mixed with three kinds of minerals: calcium, phosphorous, and potassium. The per




kilo cost of dog food A and dog food B are P 20.00 and P 16.00, respectively, whereas the minimum




requirement of calcium, phosphorous and potassium are 75, 50, and 30 units, respectively. Also, in




one kilogram of dog food A, 5 units of calcium, 2 units of phosphorous, and 3 units of potassium are




mixed. Again, in one kilogram of dog food B, 4, 6, 3 units of calcium, phosphorous, and potassium,




respectively are mixed. How many of each type of dog food must be bought to minimize the cost?

Solve the ff linear programming graphically method maximize Z= 30×, + 100ײ 4×,+6ײ≤ 90 8×, +6×, ≤100 5×,+4×,≤ 80 ×, ×, ≥ 0


1.      Solve the following linear programming problem graphically:


Minimise Z = 200 x + 500 y

subject to the constraints:

x + 2y ≥ 10 ... (1)

3x + 4y ≤ 24 ... (2)

x ≥ 0, y ≥ 0 ... (3)



A company has found that its cost to purchase a component is ETB 50 per order and the carrying cost is 10% of the average inventory. The company currently purchases ETB 20,000 worth of components in a year. Assuming that same demand will be there in the next year,



a. Suggest a suitable policy of purchase in terms of no. of orders in a year and



b. Quantity to be ordered for each year. Assuming fractional order can be made.


Draw activity network of the project.

b. Crash the activities step by step until all paths are critical.


A firm produces three products A, B, and C, each of which passes through three departments: Fabrication, Finishing and Packaging. Each unit of product A requires 3, 4 and 2 hours; a unit of B requires 5, 4 and 4 hours while each unit of product C requires 2, 4, 5 hours respectively in the three departments. Every day, 60 hours are available in fabrication department, 72 hours in the finishing department and 100 hours in the packaging department. If the unit contribution of product A is ETB 5, of product B is ETB 10, and of product C is ETB 8, determine the number of units of each of the products, which should be made each day to maximize the total contribution. Also determine if any capacity would remain unutilised.

a. Write the formulation for this linear program.

b. Solve the Linear programming problem using simplex method.


Moore’s Meatpacking Company producesahot dog mixture in 1000- pound batches. The mixturecontains two ingredients- chicken and beef.The cost per pound of each of these ingredients is asfollows:


IngredientCost/lb.

Chicken 3

Beef 5


Each batch has the following recipe requirements:

1.At least 500 pounds of chicken

2.At least 200 pounds of beef

The ratio of chicken to beef must be at least 2 to 1.


1) The company wants to know the optimalmixture of ingredientsthatwillminimizecost.

2)Formulatea linear programming model for this problem.




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