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Mathematics - Linear Operators - QM

Slixtrix Conversions, located in Waldo, Florida specializes in conversions of pick-up trucks and vans. In particular, they do a very good business in their signature line of each.

The business has three production shops which, using good project scheduling skills, work on the vehicles simultaneously. The shops are preparation, upholstery, and electric/electronics.

The company nets $5000 for each truck and $6000 for each van produced and sold. The work requirements for each, in hours, and personnel available are given in the table below. Personnel work 8 hours per day, five days per week on the conversions.

shop trucks vans personnel
preparation 8 12 10
upholstery 10 8 8
electrical 12 16 12

shop trucks vans personnel personnel hours
preparation 8 12 10 400
upholstery 10 8 8 320
electrical 12 16 12 480

trucks vans
Profit 5000 6000
Standing Order 12 10

Decision Variables
trucks vans
Units Made 20 15

Constraints

1) Hours used in each dept < hours available
Used <= Available
preparation 0 <= 400
upholstery 0 <= 320
electrical 0 <= 480

2) Total made >= standing orders
trucks vans
Units made 20 15
>= >= >=
Standing Order 12 10

3) total vans made should be less than or equal to 20
Vans made 15
<= <=
Max parts qty 20

Objective Fn
Maximize total profit
$190,000

Attachments

Solution Summary

A Complete, Neat and Step-by-step Solution is provided in the attached file.

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