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The Washington Chemical Company produces chemicals and solvents for the glue industry. The production process is divided into several "focused factories," each producing a specific set of products. The time has come to prepare the production plan for one of the focused factories. This particular factory produces five products, which must pass through both the reactor and the separator. Each product also requires a certain combination of raw materials. Production data are shown below. Product 1 2 3 4 5 Total Resources Available Resource Reactor (hr/b) Separator (hr/b) Raw Material 1 (lb) Raw Material 2 (lb) Raw Material 3 (lb) Profit contribution ($/b) 0.05 0.20 0.20 0.10 0.02 0.50 0.70 0.20 0.80 0.20 0.10 0.57 0.09 0.40 0.50 0.15 0.30 0.18 8,000 hr* 6,000 hr* 9,000 lb 5,000 lb 6,000 lb 0.10 0.40 4.00 7.00 3.50 4.00 5.70 *The total time available has been adjusted to account for setups. The five products have a prescribed sequence owing to the cost of changeovers between products. The company has a 35-day cycle (or 10 changeovers per year per product). Consequently, the time for these changeovers has been deducted from the total time available for these machines. The Washington Chemical Company has a long-term contract with a major glue manufacturer that requires annual production of 2,500 pounds of both products 3 and 4. More of these products could be produced because demand currently exceeds production capacity. a. Assume that the objective is to maximize profits. = Let X1 = annual production quantity of product 1, X2 = annual production quantity of product 2, X3 = annual production quantity of product 3, X 4 = annual production quantity of product 4, Xg = annual production quantity of product 5. = A linear programming software shows that the optimal values for X1, X2, and Xz are: = X1 = 24,634, X2 = 5,357, X3 = 2,500. What are the optimal values for X4 and X5? X4 = X5 (enter your response rounded to the nearest whole number). (enter your response rounded to the nearest whole number). b. Assuming 10 changeovers per year, specify the lot size for each product. Xy = 0, X2=, X3 = , *4 = and X5 = = I. (Enter your responses rounded to the nearest whole number.)