Answer :

__Given Data__:

• Each piece of model A requires 9 hours of labour for fabricating and 1 hour for finishing.

• Each piece of model B requires 12 hours of labour for fabricating and 3 hours for finishing.

• The maximum number of labour hours, available for fabricating is 180

• The maximum number of labour hours, available for finishing is 30

• The company makes a profit of Rs 8000 and Rs 12000 on each piece of model A and model B respectively

__Calculation__:

Let x and y be the number of models A and models B to be manufactured respectively.

Now the profit function is P = 8000x + 12000y

We have to maximize the profit

The constraints in this situation are:

• Quantities x and y are positive

x ≥ 0; y ≥ 0

• Maximum no. of labour hours for fabricating

9x + 12y ≤ 180 or 3x + 4y ≤ 60

• Maximum no. of labour hours for finishing

x + 3y ≤ 30

We need to check at each corner points for maximum profit. Corner points in this LPP problems are (0, 0), (20,0), (0,10) and (12,6)

Profit at (0, 0),

P = 8000×0 + 12000×0 = 0

Profit at (20, 0),

P = 8000×20 + 12000×0 = Rs.1,60,000

Profit at (0, 10),

P = 8000×0 + 12000×10 = Rs.1,20,000

Profit at (12, 6),

P = 8000×12 + 12000×6 = Rs.1,68,000 (maximum)

For maximum profit 12 pieces of model A and 6 pieces of model B are to be manufactured with maximum profit of Rs.1,68,000.

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