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?

contexto.140

3 years ago

Let and be number of gold rings and chains.
According to the question,

Maximize
The feasible region determined by is given by

The corner points of feasible region are . The value of at corner points are

The maximum value of is 5440 at point .
Hence, the firm should manufacture 8 gold rings and 16 gold chains to maximize their profit.