Explanation Explanation Given: The table is: Cutting time per tent Assembly time per tent Model A 0.9 hour 0.8 hour Model B 1.8 hours 1.2 hours A company manufactures two models monthly to maximize the profit. Each month the manufacturer has no more than 864 hours of labor available in the cutting department and at most 672 hours in the assembly department. The profit come to $ 25 per tent for model A and $ 40 for model B. Calculation: Assume x be the number of model A manufactured and y be the number of model B manufactured. The given information can be summarized in a table as follows: Model A Model B Total time available Number of model manufactured x y Cutting time per tent 0.9 hour 1.8 hour ≤ 864 hours Assembly time per tent 0.8 hours 1.2 hours ≤ 672 hours Use the table to write the inequalities representing constraints as shown below: 0.9 x + 1.8 y ≤ 864 0.8 x + 1.2 y ≤ 672 Solve both the constraints and rewrite the constraints as follows: x + 2 y ≤ 960 2 x + 3 y ≤ 1680 The number of models manufactured cannot be negative, Thus x ≥ 0 and y ≥ 0 The objective function, gives the total profit which is to be maximized. If the variable z represents the total profit, the objective function is as shown below: z = 25 x + 40 y Represent the mathematical model for the given linear programming problem as follows: The objective function, to be maximized z = 25 x + 40 y Subject to the constraints, x + 2 y ≤ 960 2 x + 3 y ≤ 1680 x ≥ 0 y ≥ 0 Now, plot the graph for the inequality x + 2 y ≤ 960 as shown below: Now, plot the graph for the inequality 2 x + 3 y ≤ 1680 as shown below:

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ISBN: 9780321837240

Author: Robert F. Blitzer

Publisher: PEARSON

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Chapter 8, Problem 61RE

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To calculate: The quantity of each model that must be manufactured by a manufacturer of lightweight tents that makes two models monthly to maximize the profit. Every month the manufacturer got maximum 864 labor hours in cutting department and maximum 672 hours in the assembly department. The profit is $25 per tent for model A and $40 for model B.

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Chapter 8, Problem 60RE

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Solution Summary: The author calculates the quantity of each model that must be manufactured by a manufacturer of lightweight tents that makes two models monthly to maximize the profit.

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