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 Machine 1 time/unit $30 0.5 1.0 $50 2.0 1.0 $20 0.75 0.5 Machine 2 time/unit 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 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 20% of the units produced. a. How many units of each product should be produced to maximize the total profit contribution?
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 Machine 1 time/unit $30 0.5 1.0 $50 2.0 1.0 $20 0.75 0.5 Machine 2 time/unit 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 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 20% of the units produced. a. How many units of each product should be produced to maximize the total profit contribution?
Chapter6: Systems Of Equations And Inequalities
Section: Chapter Questions
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Transcribed Image Text:Problem 8-19
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
$30
$50
2.0
Profit/unit
$20
0.75
Machine 1 time/unit
0.5
1.0
Machine 2 time/unit
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 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 20% of the units produced.
a. How many units of each product should be produced to maximize the total profit contribution?
Product # of units
2
What is the projected weekly profit associated with your solution?
$4
Transcribed Image Text:b. How many hours of production time will be scheduled on each machine? If required, round your answers to two decimal places.
Machine Hours Schedule: Machine 1:
Hours; Machine 2:
Hours
c. What is the value of an additional hour of labor? If required, round your answers to two decimal places.
$
d. Assume that labor capacity can be increased to 120 hours. Develop the optimal product mix, assuming that the extra hours are made
available.
Product # of units
2
3
Profit: $
Would you be interested in using the additional 20 hours available for this resource?
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