Q27 of 52 Page 1

A manufacturer has employed 5 skilled men and 10 semi-skilled men and makes two models A and B of an article. The making of one item of model A requires 2 hours work by a skilled man and 2 hours work by a semi-skilled man. One item of model B requires 1 hour by a skilled man and 3 hours by a semi-skilled man. No man is expected to work more than 8 hours per day. The manufacturer’s profit on an item of model A is ₹15 and on an item of model B is ₹10. How many of items of each model should be made per day in order to maximize profit? Formulate the above LPP and solve it graphically and find the maximum profit.

Let x and y be the number of items produced per day of model A and model B respectively.


Then, 2x+y≤40


2x+3y≤80


x≥0, y≥0


We have to maximize Z:15x+10y



Since the area is bounded, therefore the maximum value will occur on corner points.


When x=0 and y=0, Z=0


When x=20 and y=0, Z=300


When x=0 and ,


When x=10 and y=20, Z=350


Hence the maximum profit that the manufacturer can make in a day is ₹350, when the number of items of model A will be 10 and of model B will be 20.


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