Subject to constraints, C(0,20) X 0, y≥ 0 20 B(20,10) ≥ 200x + 100y 5000 => 2x + y 50 0 A(25,0) X ≤ ≤ And 25x + 50y 1000 =>x + 2y 40 25 40 ≤ ≤ Z = x+ y VALUE A(25, 0) 25 + 0 25 B(20, 10) 20 + 10 30 maximum C(0, 20) 0 +20 20 Z is maximum at B (20, 10) Hence, 20 cakes of type 1 and 10 cakes of type 2 must be made for maximum number of 30 cakes. A Manufacturing company makes two models A and B of a product. Each piece of model A requires 9 labour hours for fabricating and 1 labour hour for finishing. Each piece of model B requires 12 labour hours for fabricating and 3 labour hour for finishing. For Fabricating and finishing, the maximum labour hours available are 180 and 30 respectively. The company makes a profit of Rs 8000 on each piece of model A and Rs 12000 on each piece of Model B. How many pieces of model A and Model B should be manufactured per week to realise a maximum profit ? What is the maximum profit per week ? Sol: Suppose x is the number of pieces of model A and y is the number of pieces of Model B. Then Total profit (in Rs ) = 8000x + 12000y Y Maximize Z = 8000x + 12000y Subject to the constraints: 9x + 12y 180 C(0,10) B(12,6) ≤ => 3x + 4y 60 ≤ X + 3y 30 0 A(20,0) X ≤ X 0, y 0 ≥ ≥ CORNER POINT Z = 8000x + 12000y 0(0, 0) 0 A(20, 0) 160000
Subject to constraints, C(0,20) X ≥ 0, y≥ 0 20 B(20,10) 200x + 100y ≤ 5000 => 2x + y ≤ 50 0 A(25,0) X And 25x + 50y ≤ 1000 =>x + 2y ≤ 40 25 40 Z = x+ y VALUE A(25, 0) 25 + 0 25 B(20, 10) 20 + 10 30 maximum C(0, 20) 0 +20 20 Z is maximum at B (20, 10) Hence, 20 cakes of type 1 and 10 cakes of type 2 must be made for maximum number of 30 cakes. A Manufacturing company makes two models A and B of a product. Each piece of model A requires 9 labour hours for fabricating and 1 labour hour for finishing. Each piece of model B requires 12 labour hours for fabricating and 3 labour hour for finishing. For Fabricating and finishing, the maximum labour hours available are 180 and 30 respectively. The company makes a profit of Rs 8000 on each piece of model A and Rs 12000 on each piece of Model B. How many pieces of model A and Model B should be manufactured per week to realise a maximum profit ? What is the maximum profit per week ? Sol: Suppose x is the number of pieces of model A and y is the number of pieces of Model B. Then Total profit (in Rs ) = 8000x + 12000y Y Maximize Z = 8000x + 12000y Subject to the constraints: 9x + 12y ≤ 180 C(0,10) B(12,6) => 3x + 4y ≤ 60 X + 3y ≤ 30 0 A(20,0) X X ≥ 0, y ≥ 0 CORNER POINT Z = 8000x + 12000y 0(0, 0) 0 A(20, 0) 160000
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