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10. A can of cat food, guaranteed by the manufacturer to contain at least 10 units of protein, 20 units of mineral matter, and 6 units of fat, consists of a mixture of four different ingredients. Ingredient A contains 10 units of protein, 2 units of mineral matter, and 1 2 unit of fat per 100g. Ingredient B contains 1 unit of protein, 40 units of mineral matter, and 3 units of fat per 100g. Ingredient C contains 1 unit of protein, 1 unit of mineral matter, and 6 units of fat per 100g. Ingredient D contains 5 units of protein, 10 units of mineral matter, and 3 units of fat per 100g. The cost of each ingredient is Birr 3, Birr 2, Birr 1, and Birr 4 per 100g, respectively. How many grams of each should be used to minimize the cost of the cat food, while still meeting the guaranteed composition? (Hint: Solve through simplex model)
A firm manufactures two products; the net profit on product 1 is Birr 3 per unit and Birr 5 per unit on product 2. The manufacturing process is such that each product has to be processed in two departments D1 and D2. Each unit of product1 requires processing for 1 minute at D1 and 3 minutes at D2; each unit of product 2 requires processing for 2 minutes at D1 and 2 minutes at D2. Machine time available per day is 860 minutes at D1 and 1200 minutes at D2. How much of product 1 and 2 should be produced every day so that total profit is maximum. (solve with graphical method) Q3. Solve the following LP problem by graphical method: Maximise Z = 300X1 + 700X2 Subject to the constraints: X1 + 4X2 ≤ 20 2X1 + X2 ≤ 30 X1 + X2 ≤ 8 And X1, X2 ≥ 0 Q4.
A company manufactures two products X and Y. Each product has to be processed in three departments: welding, assembly and painting. Each unit of X spends 2 hours in the welding department, 3 hours in assembly and 1 hour in painting. The corresponding times for a unit of Y are 3, 2 and 1 respectively. The man-hours available in a month are 1500 for the welding department, 1500 in assembly and 550 in painting. The contribution to profits are $100 for product X and $120 for product Y.
Formulate the appropriate linear programming problem
Solve it graphically to obtain the optimal solution for the maximum contribution
A firm manufactures two products; the net profit on product 1 is Birr 3 per unit and Birr 5 per unit on product 2. The manufacturing process is such that each product has to be processed in two departments D1 and D2. Each unit of product1 requires processing for 1 minute at D1 and 3 minutes at D2; each unit of product 2 requires processing for 2 minutes at D1 and 2 minutes at D2. Machine time available per day is 860 minutes at D1 and 1200 minutes at D2. How much of product 1 and 2 should be produced every day so that total profit is maximum. (solve with graphical method)
Solve the following LP problem by graphical method: Maximise Z = 300X1 + 700X2
Subject to the constraints: X1 + 4X2 ≤ 20 2X1 + X2 ≤ 30 X1 + X2 ≤ 8 And X1, X2 ≥ 0
firm manufactures two products; the net profit on product 1 is Birr 3 per unit and Birr 5
per unit on product 2. The manufacturing process is such that each product has to be
processed in two departments D1 and D2. Each unit of product1 requires processing for 1
minute at D1 and 3 minutes at D2; each unit of product 2 requires processing for 2 minutes
at D1 and 2 minutes at D2. Machine time available per day is 860 minutes at D1 and 1200
minutes at D2. How much of product 1 and 2 should be produced every day so that total
profit is maximum. (solve with graphical method)
A pharmacy has determined that a healthy person should receive 70 units of proteins, 100 units of carbohydrates and 20 units of fat daily. If the store carries the six types of health food with their ingredients as shown in the table below, what blend of foods satisfies the requirements at minimum cost to the pharmacy? Make the mathematical mod
The crumb and Custard bakery makes cakes and pies. The main ingredients are flour and sugar. The following linear programming model has been developed for determining the number of cakes and pies (x1 and x2 to produce each day to maximize profit.
Max Z=x1 + 5x2
Subject to:
8x1+10x2< 25(flour, lb)
2x1+4x2< 16(sugar, lb)
x1< 5(demand for cakes)
x1,x2 >0
Solve this model using simplex method.
Solve the following LPP:
Minimize Z= 120x1+60x2
Subject to:
20x1+30x2>= 900
40x1+30x2>=1200
x1,x2>=0
A merchant plans to sell two types of personal computers – a desktop model and a portable model that will cost Birr 25000 and Birr 40000 respectively. He estimates that the total monthly demand of computers will not exceed 250 units. Determine the number of units of each type of computers which the merchant should stock to get maximum profit if he does not want to invest more than Birr 70 lakhs and if his profit on the desktop model is Birr 4500 and on portable model is Birr 5000. (Find optimal Solution by simplex Model)
