Answer to Question #254584 in Operations Research for Rossy

Question

1.      A jewelry store makes necklaces and bracelets from gold and platinum. The store has 18 ounces of gold and 20 ounces of platinum. Each necklace requires 3 ounces of gold and 2 ounces of platinum, whereas each bracelet requires 2 ounces of gold and 4 ounces of platinum. The demand for bracelets is no more than four. A necklace earns $300 in profit and a bracelet, $400. The store wants to determine the number of necklaces and bracelets to make in order to maximize profit. a. Formulate a linear programming model for this problem. b. Solve this model by using graphical analysis.

Answer 1

A)Formulate a linear programming model for this problem

Maximize profit=$300x_{1}+400x_{2}$

Subject to:

$3x_{1}+2x_{2}\leq18$ ​(gold, oz)

$2x_{1}+4x_{2}\leq20$ ​(platinum, oz)

$x_{2}\leq4$ ​(demand, bracelets)

$x_{1} ,x_{2}\ge0$

B) Solving this model using graphical analysis

Point A:

$x_{1}=0$

$x_{2}=4$

profit=1600

Point B:

$x_{1}=2$

$x_{2}=4$

profit=2200

Point C:

$x_{1}=4$

$x_{2}=3$

profit=2400

Point D:

$x_{1}=6$

$x_{2}=0$

profit=1800

In order to maximize profit, the optimal point is chosen. Point C which yields a profit of 2400 is the optimal point.