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 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. Formulate the above as a LP problem with the ratio and other constraints and decision variables.

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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 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. Formulate the above as a LP problem with the ratio and other constraints and decision
variables.

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