The CZ Jewelry Company Produces Two Products: (1) Engagement Rings

Essay

The CZ Jewelry Company produces two products: (1) engagement rings and (2) jeweled watches. The production process for each is similar in that both require a certain number of hours of diamond work and a certain number of labor hours in the gold department. Each ring takes four hours of diamond work and two hours in the gold shop. Each watch requires three hours in diamonds and one hour in the gold department. There are 240 hours of diamond labor available and 100 hours of gold department time available for the next month. Each engagement ring sold yields a profit of $9; each watch produced may be sold for a $10 profit.
a. Give a complete formulation of this problem, including a careful definition of your decision variables. Let the first decision variable, (X₁), deal with rings, the second decision variable, (X₂), with watches, the first constraint with diamonds, and the second constraint with gold.
b. Graph the problem fully in the following space. Label the axes carefully, plot the constraints, shade the feasibility region, plot at least one isoprofit line that reveals the optimal solution, circle the corner points and highlight the optimal corner point so found, and solve for it algebraically. (Show all your work to get credit.)