Answer :

Let x articles of deluxe model and y articles of an ordinary model be made.

Numbers cannot be negative.

Therefore,

x, y 0

According to the question, the profit on each model of deluxe and ordinary type model are Rs 15 and Rs 10 respectively.

So, profits on x deluxe model and y ordinary models are 15x and 10y.

Let Z be total profit, then,

Z = 15x + 10y

Since, the making of a deluxe and ordinary model requires 2 hrs. and 1 hr work by skilled men, so, x deluxe and y ordinary models require 2x and y hours of skilled men but time available by skilled men is 58 = 40 hours.

So,

2x + y 40 { First Constraint}

Since, the making of a deluxe and ordinary model requires 2 hrs. and 3 hrs work by semi skilled men, so, x deluxe and y ordinary models require 2x and 3y hours of skilled men but time available by skilled men is 108 = 80 hours.

So,

2x + 3y 80 {Second constraint}

Hence the mathematical formulation of LPP is,

Max Z = 15x + 10y

subject to constraints,

2x + y 40

2x + 3y 80

x, y 0

Region 2x + y 40: line 2x + 4y = 40 meets axes at (20,0), (0,40) respectively. Region containing origin represents 2x + 3y 40 as (0,0) satisfies 2x + y 40

Region 2x + 3y 80: line 2x + 3y = 80 meets axes at (40,0), (0,) respectively. Region containing origin represents 2x + 3y 80.

The corner points are (20,0), P(10,20), (0,).

The value of Z = 15x + 10y at these corner points are

The maximum value of Z is 300 which is attained at P(10,20).

Thus, maximum profit is obtained when 10 units of deluxe model and 20 units of ordinary model is produced.

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