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Problem 3-19 (Algorithmic) 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 Profit/unit Machine 1 time/unit Machine 2 time/unit Product 1 2 wo 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 90 labor-hours is available for assignment to the machines during the coming week. Other production requirements are that product 1 annot account for more than 50% of the units produced and that product 3 must account for at least 10% of the units produced. . How many units of each product should be produced to maximize the total profit contribution? If required, round your answers to the nearest whole number. If your answer is zero, enter "0". 3 Profit S What is the projected weekly profit associated with your solution? Machine Hours Schedule: Machine 1 Machine 2 of units Product Product 1 $39 0.5 . How many hours of production time will be scheduled on each machine? 1 2 3 1 c. What is the value of an additional hour of labor? If required, round your answer to two decimal places. Profit S Product 2 $51 1.5 2.5 $ d. Assume that labor capacity can be increased to 100 hours. Develop the optimal product mix, assuming that the extra hours are made available. If required, round non-monetary answers to the nearest whole number. If required, round monetary answer to the nearest dollar. If your answer is zero, enter "0". of units Hours Hours 1 Product 3 $18 1 1 Would you be interested in using the additional 10 hours available for this resource?

Problem 3-19 (Algorithmic) 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 Profit/unit Machine 1 time/unit Machine 2 time/unit Product 1 2 wo 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 90 labor-hours is available for assignment to the machines during the coming week. Other production requirements are that product 1 annot account for more than 50% of the units produced and that product 3 must account for at least 10% of the units produced. . How many units of each product should be produced to maximize the total profit contribution? If required, round your answers to the nearest whole number. If your answer is zero, enter "0". 3 Profit S What is the projected weekly profit associated with your solution? Machine Hours Schedule: Machine 1 Machine 2 of units Product Product 1 $39 0.5 . How many hours of production time will be scheduled on each machine? 1 2 3 1 c. What is the value of an additional hour of labor? If required, round your answer to two decimal places. Profit S Product 2 $51 1.5 2.5 $ d. Assume that labor capacity can be increased to 100 hours. Develop the optimal product mix, assuming that the extra hours are made available. If required, round non-monetary answers to the nearest whole number. If required, round monetary answer to the nearest dollar. If your answer is zero, enter "0". of units Hours Hours 1 Product 3 $18 1 1 Would you be interested in using the additional 10 hours available for this resource?

Practical Management Science
Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter4: Linear Programming Models
Section4.8: Data Envelopment Analysis (dea)
Problem 42P
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Problem 3-19 (Algorithmic) 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 Profit/unit Machine 1 time/unit Machine 2 time/unit Product 1 2 3 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 90 labor-hours is available for 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 10% of the units produced. a. How many units of each product should be produced to maximize the total profit contribution? If required, round your answers the nearest whole number. If your answer is zero, enter "0". Profit = $ $ Machine 2 What is the projected weekly profit associated with your solution? Machine Hours Schedule: Machine 1 # of units Product Product 1 b. How many hours of production time will be scheduled on each machine? 1 2 $39 0.5 3 Profit = $ 1 c. What is the value of an additional hour of labor? If required, round your answer to two decimal places. # of units Product 2 $51 1.5 Hours 2.5 Hours d. Assume that labor capacity can be increased to 100 hours. Develop the optimal product mix, assuming that the extra hours are made available. If required, round non-monetary answers to the nearest whole number. If required, round monetary answer to the nearest dollar. If your answer is zero, enter "0". Product 3 $18 1 1 Would you be interested in using the additional 10 hours available for this resource?
Transcribed Image Text:Problem 3-19 (Algorithmic) 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 Profit/unit Machine 1 time/unit Machine 2 time/unit Product 1 2 3 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 90 labor-hours is available for 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 10% of the units produced. a. How many units of each product should be produced to maximize the total profit contribution? If required, round your answers the nearest whole number. If your answer is zero, enter "0". Profit = $ $ Machine 2 What is the projected weekly profit associated with your solution? Machine Hours Schedule: Machine 1 # of units Product Product 1 b. How many hours of production time will be scheduled on each machine? 1 2 $39 0.5 3 Profit = $ 1 c. What is the value of an additional hour of labor? If required, round your answer to two decimal places. # of units Product 2 $51 1.5 Hours 2.5 Hours d. Assume that labor capacity can be increased to 100 hours. Develop the optimal product mix, assuming that the extra hours are made available. If required, round non-monetary answers to the nearest whole number. If required, round monetary answer to the nearest dollar. If your answer is zero, enter "0". Product 3 $18 1 1 Would you be interested in using the additional 10 hours available for this resource?
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