A small firm manufactures necklace and bracelets. The total number of necklace and bracelet that it can handle per day is at most 24. It takes 1 hour to make a bracelet and half an hour to make a necklace. The maximum number of hours available per day is 16 . If the profit on a necklace is and that on a bracelet is , how many of each should be produced daily to maximize the profit? It is being given that at least one of each must be produced.

contexto.140

3 years ago

Let the firm manufacture number of necklaces and y number of bracelets a day.
According to the question,

Maximize
The feasible region determined by is given by

The corner points of the feasible region are . The number of bracelets should be whole number. Therefore, considering point The value of at corner point is

The maximum value of is 4700 at point .
The firm should make 2 necklaces and 15 bracelets.