The CZ Jewelry Company produces two products I engagement ri

The CZ Jewelry Company produces two products: (I) 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 Formulate this as a Linear Programming problem. Clearly define the Decision Variables, Objective and the Constraints A small oil company has a refining budget of $200,000 and would like to determine the optimal production plan for profitability. The following table lists the costs associated with its three products Marketing has a budget of $50,000, and the company has 750,000 gallons of crude oil available . each gallon of gasoline contributes 14 cents of profits, heating oil provides 10 cents, and plastic resin 30 cents per unit. The refining process results in a ratio of two units of heating oil for each unit of gasoline produced. This problem has been modeled as a linear programming problem and solved on the computer The Linear Programming formulation of the above problem is as follows: Define, Xi= gallons of gasoline refined X_2=gallons of heating oil refined X_3= gallons of plastic resin refined Objective: Max:.144Xi + .10x_2 + .30x_3 Constraints: .40X1 +.10x_2+ 6Ox_3 LE 200,000 .10X1 + .05x_2 + .07x_3 LE 50,000 10X1 + 5x_2 + 20x_3 LE 750,000 X_2 - 2X1 =0 Refining budget Marketing budget Crude oil available Ratio X_1, X_2, X_3> 0

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