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 $\pm 100$ and that on a bracelet is $\pm 300$, 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.

Home » 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.

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 $\pm 100$ and that on a bracelet is $\pm 300$ , 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.

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 $\pm 100$ and that on a bracelet is $\pm 300$ , 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.

Let the firm manufacture $x$ number of necklaces and y number of bracelets a day.
$\therefore$ According to the question,
$x+y \leq 24,0.5 x+y \leq 16 x \geq 1, y \geq 1$
Maximize $Z=100 x+300 y$
The feasible region determined by $x+y \leq 24,0.5 x+y \leq 16, x \geq 1, y \geq 1$ is given by

The corner points of the feasible region are $A(1,1), B(1,15.5), C(16,8), D(23,1)$ . The number of bracelets should be whole number. Therefore, considering point $(2,15) .$ The value of $Z$ at corner point is