Question 91) Susanna Nanna is the production manager for a

91) Susanna Nanna is the production manager for a furniture manufacturing company. The company produces tables (X) and chairs (Y). Each table generates a profit of $80 and requires 3 hours of assembly time and 4 hours of finishing time. Each chair generates $50 of profit and requires 3 hours of assembly time and 2 hours of finishing time. There are 360 hours of assembly time and 240 hours of finishing time available each month. The following linear programming problem represents this situation.

Maximize 80X + 50Y

Subject to: 3X + 3Y ? 360

4X + 2Y ? 240

X, Y ? 0

The optimal solution is X = 0, and Y = 120.

(a) What would the maximum possible profit be?

(b) How many hours of assembly time would be used to maximize profit?

(c) If a new constraint, 2X + 2Y ? 400, were added, what would happen to the maximum possible profit?

92) As a supervisor of a production department, you must decide the daily production totals of a certain product that has two models, the Deluxe and the Special. The profit on the Deluxe model is $12 per unit, and the Special’s profit is $10. Each model goes through two phases in the production process, and there are only 100 hours available daily at the construction stage and only 80 hours available at the finishing and inspection stage. Each Deluxe model requires 20 minutes of construction time and 10 minutes of finishing and inspection time. Each Special model requires 15 minutes of construction time and 15 minutes of finishing and inspection time. The company has also decided that the Special model must comprise at most 60 percent of the production total.

Formulate this as a linear programming problem.

93) Determine where the following two constraints intersect.

5X + 23Y ? 1000

10X + 26Y ? 1600

94) Determine where the following two constraints intersect.

2X – 4Y = 800

?X + 6Y ? -200

95) Two advertising media are being considered for promotion of a product. Radio ads cost $400 each, while newspaper ads cost $600 each. The total budget is $7,200 per week. The total number of ads should be at least 15, with at least 2 of each type, and there should be no more than 19 ads in total. The company does not want the number of newspaper ads to exceed the number of radio ads by more than 25 percent. Each newspaper ad reaches 6,000 people, 50 percent of whom will respond; while each radio ad reaches 2,000 people, 20 percent of whom will respond. The company wishes to reach as many respondents as possible while meeting all the constraints stated. Develop the appropriate LP model for determining the number of ads of each type that should be placed.

96) Suppose a linear programming (maximization) problem has been solved and the optimal value of the objective function is $300. Suppose a constraint is removed from this problem. Explain how this might affect each of the following:

(a) the feasible region.

(b) the optimal value of the objective function.

97) Consider the following constraints from a two-variable linear program.

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