Number of Necklaces and Bracelets to Maximize Profit Questions

A Tiffany & Co. 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 4. A necklace earns $400 in profits and a bracelet, $700. To maintain product diversity, the store wants that the number of bracelets produced must be no more than 2/3 of total production. The store wants to determine the number of necklaces and bracelets to make in order to maximize profit. Assume that it is possible to produce necklaces or bracelets in fractional quantities.

1) Formulate a linear programming model for this problem.
2) Sketch the feasible region.
3) Find the optimal solution and resultant profit using the graphical method
4) Which constraints are binding?
5) What happens if the profit of necklace increases to $500?

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