A manufacturing company makes two types of teaching aids A and B of Mathematics for class XII. Each piece of type A requires 9 labour hours for fabricating and 1 labour hour for finishing. Each piece of type B requires 12 labour hours for fabricating and 3 labour hours for finishing. For fabricating and finishing, the maximum labour hours available per week are 180 and 30 respectively. The company makes a profit of Rs. 80 on each piece of type A and Rs. 120 on each piece of type B. How many pieces of type A and type B should be manufactured per week to get a maximum profit? Make it as an LPP and solve graphically. What is the maximum profit per week?
Answer: Max profit = Rs 1680 at (12, 6): 12 pieces of type A and 6 of type B
Solution
Let x pieces of type A and y pieces of type B be made per week. Profit: Z=80x+120y. Fabricating: 9x+12y≤180⟹3x+4y≤60 Finishing: x+3y≤30 x≥0,y≥0 Corner points: (0,0), (20,0), (12,6) (intersection of 3x+4y=60 and x+3y=30) and (0,10). Evaluate Z=80x+120y: (20,0): Z=1600 (12,6): Z=960+720=1680 ← maximum (0,10): Z=1200
∴Zmax=Rs 1680 at (12,6)
12 pieces of type A and 6 pieces of type B give the maximum profit of Rs 1680 per week.Feasible region for 3x + 4y = 60 and x + 3y = 30, with corner points (0, 0), (20, 0), (12, 6) and (0, 10).
