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Better Products, Inc., manufactures three products on two machines. In a typical week, 40 hours are available on each machine. The profit contribution and production time in hours per unit are as follows: Category Product 1 Product 2 Product 3 Profit/unit $30 $50 $20 Machine 1 time/unit 0.5 2.0 0.75 Machine 2 time/unit 1.0 1.0 0.5 Two operators are required for machine 1-thus, 2 hours of labor must be scheduled for each hour of machine 1 time. Only one operator is required for machine 2. A maximum of 100 labor-hours is available f assignment to the machines during the coming week. Other production requirements are that product 1 cannot account for more than 50% of the units produced and that product 3 must account for at least 2 of the units produced. (a) How many units of each product should be produced to maximize the total profit contribution? What is the projected weekly profit (in $) associated with your solution? Product 1 25 Product 2 Product 3 25 weekly profit $ 1250 (b) How many hours of production time will be scheduled on each machine? 31.25 37.5 machine 1 v hr machine 2 v hr (c) What is the value (in $) of an additional hour of labor? $ 25

Better Products, Inc., manufactures three products on two machines. In a typical week, 40 hours are available on each machine. The profit contribution and production time in hours per unit are as follows: Category Product 1 Product 2 Product 3 Profit/unit $30 $50 $20 Machine 1 time/unit 0.5 2.0 0.75 Machine 2 time/unit 1.0 1.0 0.5 Two operators are required for machine 1-thus, 2 hours of labor must be scheduled for each hour of machine 1 time. Only one operator is required for machine 2. A maximum of 100 labor-hours is available f assignment to the machines during the coming week. Other production requirements are that product 1 cannot account for more than 50% of the units produced and that product 3 must account for at least 2 of the units produced. (a) How many units of each product should be produced to maximize the total profit contribution? What is the projected weekly profit (in $) associated with your solution? Product 1 25 Product 2 Product 3 25 weekly profit $ 1250 (b) How many hours of production time will be scheduled on each machine? 31.25 37.5 machine 1 v hr machine 2 v hr (c) What is the value (in $) of an additional hour of labor? $ 25

College Algebra (MindTap Course List)
College Algebra (MindTap Course List)
12th Edition
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:R. David Gustafson, Jeff Hughes
Chapter6: Linear Systems
Section6.8: Linear Programming
Problem 5SC: If during the following year it is predicted that each comedy skit will generate 30 thousand and...
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Better Products, Inc., manufactures three products on two machines. In a typical week, 40 hours are available on each machine. The profit contribution and production time in hours per unit are as follows: Category Product 1 Product 2 Product 3 Profit/unit $30 $50 $20 Machine 1 time/unit 0.5 2.0 0.75 Machine 2 time/unit 1.0 1.0 0.5 Two operators are required for machine 1-thus, 2 hours of labor must be scheduled for each hour of machine 1 time. Only one operator is required for machine 2. A maximum of 100 labor-hours is available fe assignment to the machines during the coming week. Other production requirements are that product 1 cannot account for more than 50% of the units produced and that product 3 must account for at least 2 of the units produced. (a) How many units of each product should be produced to maximize the total profit contribution? What is the projected weekly profit (in $) associated with your solution? Product 1 25 Product 2 Product 3 25 weekly profit $ 1250 (b) How many hours of production time will be scheduled on each machine? machine 1 31.25 hr machine 2 37.5 hr (c) What is the value (in $) of an additional hour of labor? $ 25 (d) Assume that labor capacity can be increased to 180 hours. Develop the optimal product mix and the projected weekly profit (in $), assuming the extra hours are made available. Product 1 Product 2 Product 3 weekly profit $ Would you be interested in using the additional 80 hours available for this resource?
Transcribed Image Text:Better Products, Inc., manufactures three products on two machines. In a typical week, 40 hours are available on each machine. The profit contribution and production time in hours per unit are as follows: Category Product 1 Product 2 Product 3 Profit/unit $30 $50 $20 Machine 1 time/unit 0.5 2.0 0.75 Machine 2 time/unit 1.0 1.0 0.5 Two operators are required for machine 1-thus, 2 hours of labor must be scheduled for each hour of machine 1 time. Only one operator is required for machine 2. A maximum of 100 labor-hours is available fe assignment to the machines during the coming week. Other production requirements are that product 1 cannot account for more than 50% of the units produced and that product 3 must account for at least 2 of the units produced. (a) How many units of each product should be produced to maximize the total profit contribution? What is the projected weekly profit (in $) associated with your solution? Product 1 25 Product 2 Product 3 25 weekly profit $ 1250 (b) How many hours of production time will be scheduled on each machine? machine 1 31.25 hr machine 2 37.5 hr (c) What is the value (in $) of an additional hour of labor? $ 25 (d) Assume that labor capacity can be increased to 180 hours. Develop the optimal product mix and the projected weekly profit (in $), assuming the extra hours are made available. Product 1 Product 2 Product 3 weekly profit $ Would you be interested in using the additional 80 hours available for this resource?
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