Question 2

A factory makes rings and watches from silver and gold. The factory has 18 ounces of silver and 20 ounces of gold. Each rings requires 3 ounces of silver and 2 ounces of gold, whereas each watches requires 2 ounces of silver and 4 ounces of gold. The demand for watches is no more than four. A rings earns $300 in profit and a watches, $400. The factory wants to determine the number of rings and watches to make in order to maximize profit.

a. Formulate a linear programming model for this problem and solve this by using graphical analysis. Also, explain the effect on the optimal solution of increasing the profit on a watch from $400 to $600. What will be the effect of changing the gold requirement for a ring from 2 ounces to 3 ounces?

b. The maximum demand for watches is four. If the store produces the optimal number of watches and rings, will the maximum demand for watches be met? If not, by how much will it be missed?

c. What profit for a ring would result in no watches being produced, and what would be the optimal solution for this profit?

d. Demonstrate above questions by using Excel.