Formulate and use linear programming to solve the following problem. A firm wants to determine how many units of each of two products (products X and Y) they should produce in order to make the most money. The profit from making a unit of product X is $100 and the profit from making a unit of product Y is $80. Although the firm can readily sell any amount of either product, it is limited by its total labor hours and total machine hours available. The total labor hours per week are 800. Product X takes 4 hours of labor per unit and Product Y takes 2 hours of labor per unit. The total machine hours available are 750 per week. Product X takes 1 machine hour per unit and Product Y takes 5 machine hours per unit. Write the constraints and the objective function for this problem, solve for the best mix of product X and Y, and report the maximum value of the objective function

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Business

Newton

25 April, 01:13

Formulate and use linear programming to solve the following problem. A firm wants to determine how many units of each of two products (products X and Y) they should produce in order to make the most money. The profit from making a unit of product X is $100 and the profit from making a unit of product Y is $80. Although the firm can readily sell any amount of either product, it is limited by its total labor hours and total machine hours available. The total labor hours per week are 800. Product X takes 4 hours of labor per unit and Product Y takes 2 hours of labor per unit. The total machine hours available are 750 per week. Product X takes 1 machine hour per unit and Product Y takes 5 machine hours per unit. Write the constraints and the objective function for this problem, solve for the best mix of product X and Y, and report the maximum value of the objective function

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Skylar Sampson · Answer 1

Objective function: Maximize Z = $100 X + $80 Y.

Subject to:

4 X + 2 Y < = 800

1 X + 5 Y < = 750

Explanation:

The total labor hours per week are 800. Product X takes 4 hours of labor per unit and Product Y takes 2 hours of labor per unit.

4 X + 2 Y < = 800

The total machine hours available are 750 per week. Product X takes 1 machine hour per unit and Product Y takes 5 machine hours per unit.

1 X + 5 Y < = 750,

X = 138.89

Y = 122.22

Z = $23,666.67