Q. 65.0( 1 Vote )

# A small manufactu

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 5 8 = 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 10 8 = 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.

Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation view all courses RELATED QUESTIONS :

A manufacturer prMathematics - Board Papers

A retired person Mathematics - Board Papers

A manufacturing cMathematics - Board Papers