Q17 of 97 Page 1376

A small manufacture has employed 5 skilled men and 10 semiskilled men and makes an article in two qualities, a deluxe model and an ordinary model. The making of a deluxe model requires 2hours work by a skilled man and 2hours work by a semiskilled man. The ordinary model requires 1 hour by a skilled man and 3 hours by a semiskilled man. By union rules, no man can work more than 8 hours per day. The manufacture gains ₹15 on the deluxe model and ₹10 on the ordinary model. How many of each type should be made in order to maximize his total daily profit? Also, find the maximum daily profit.


Let x and y be number of deluxe article manufactured and ordinary article manufactured.


∴According to the question,


2x + y , 2x + 3y


Maximize Z = 15x + 10y


The feasible region determined by 2x + y , 2x + 3y is given by



The corner points of feasible region are A(0,0) , B(0,80/3) , C(10,20),D(20,0).


The value of Z at corner points are



The maximum value of Z is 350 at point (10,20).


Hence, the manufacturer should produce 10 types of deluxe article and 20 types of ordinary article to make maximum profit of Rs.350.


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