A small firm manufactures gold rings and chains. The combined number of rings and chains manufactured per day is at most 24. It takes 1 hour to make a ring and half an hour for a chain. The maximum number of hour to available per day is 16. If the profit on a ring is ₹300 and that on a chain is ₹190, how many of each should be manufactured daily so as to maximize the profit?


Let x and y be number of gold rings and chains.


According to the question,


x + y , x + 0.5y


Maximize Z = 300x + 190y


The feasible region determined by x + y , x + 0.5y is given by



The corner points of feasible region are A(0,0) , B(0,24) , C(8,16), D(16,0).The value of Z at corner points are



The maximum value of Z is 5440 at point (8,16).


Hence, the firm should manufacture 8 gold rings and 16 gold chains to maximize their profit.


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