- A factory manufactures two products A & B. To manufacture A, a certain machine needs to be operated for 1.5 hrs. & in addition the craftsman has to work on it for another 2.0 hrs. To manufacture B, the times are 2.5 hrs. & 1.5 hrs. respectively. In a week, the factory has 80 hrs. of machine time & 70 hrs. of craftsman time. Profit per unit for A is Rs. 6 & for B is Rs. 4. Find product mix for maximum profit. Formulate as LPP and solve graphically.

- Vitamin B1 & B2 are found in two different foods F1 & F2. 1 unit of F1 contains 2 units of B1 & 3 units of B2. 1 unit of F2 contains 4 units of B1 & 2 units of B2. Cost per unit is 5.5 for F1 & 2.5 for F2. Minimum daily requirement is 40 for B1 & 50 for B2. Find optimal mix of B1 & B2 at minimum cost.

- A company makes two products A, B. Cost of production for A – 55 & for B – 80 per unit. Minimum supply of B is 200 units. One unit of A requires 1 machine hr. Total machine hrs. available for A are 400. No limit on available machine hrs. for B. Both A & B need 1 labour hr. per unit. Total labour hrs. are 500. Formulate as LPP to minimize cost.

- A company manufactures two products A & B. Both the products pass through two machines M1 & M2. The time required to process 1 unit for A & B on each machine & available quantity of each machine hours is as below –

ProductÂ Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â M1Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â M2Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Profit per unit (Rs.)

AÂ Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â 6Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â 2Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â 28

BÂ Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â 4Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â 4Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â 20

Max. CapacityÂ Â Â Â Â Â Â Â Â Â Â Â 3600Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â 2000

Material availability of material is sufficient to produce only 500 units of A & 400 units of B.

Solve graphically to determine maximum profit.

- A firm makes two products P1 & P2. It has production capacity of 18 tons per day. The firm must supply at least 4 tons of P1 and at least 6 tons of P2 per day. Each ton of P1 & P2 require 60 hrs of machine work each. Total machine hrs are 750. Profit per ton of P1 is Rs. 160 and for P2 is Rs. 240. Solve graphically and find optimal solution.

- A firm does animal breeding. Various products & nutrients are fed to animals. A & B are nutrients.

**Â Â Â Â Â Â Â Â Â Â Â Nutrient ConstituentsÂ Â Â Â Â Â Â Â Â Â Quantity per unitÂ Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Minimum requirement**

**Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â AÂ Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â B**

1Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â 36Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â 6Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â 110

2Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â 3Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â 12Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â 36

__Â Â Â Â Â Â Â Â Â Â Â 3Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â 20Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â 10Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â 100__

Cost per unit (Rs.)Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â 20Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â 40

Determine minimum cost at which minimum requirement of nutrition can be achieved. Solve graphically.

7.. A firm produces two products P & Q. Maximum total daily production is 600 units. But at least total 300 units must be produced daily. Per unit machine hrs are 6 for P and 2 for Q. At least 1200 machine hrs are to be used daily. Manufacturing cost per unit is Rs. 45 for P and Rs. 20 for Q. Solve graphically.

- Total production capacity 9 T per day, two products X, Y are produces which require same production capacity. The firm has to supply at least 2 T of X & 3 T of Y per day. Each T of X & Y require 20 & 50 machine hours respectively. Max. availability is 360 hrs. Profit per T is 80 for X & 110 for Y. Solve graphically to maximize profit.

- A pharmacy company produces two vitamins per day. Daily production of vitamins is 200 kg. Vitamin A costs Rs. 2 per kg & B, Rs. 5 per kg. Not more than 80 kg of A can be produced & at least 60 kg of B should be produced. Find optimal solution graphically

- A manufacture produces two different models X and Y of the same product. Model X makes a contribution of Rs. 60 per unit and model Y, Rs. 30 per unit towards total profit. Raw materials R1 and R2 are required for production.Â At least 18 kg of R1 and at least 12 kg of R2 must be used daily.Â Also at most 34 labour hours are to be utilized.Â A quantity of 2 kg of R1 is required for X and 1 kg of R1 is required for Y.Â For each of X and Y, 1 kg of R2 is required.Â It takes 3 labour hours to manufacture X and 2 labour hours to manufacture Y.Â How many units of each model should be produced to maximize the profit? Solve graphically

Source:– Vipin Saboo Tutorials

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