A small furniture manufacturer produces tables and chairs. Each product must go

Question

A small furniture manufacturer produces tables and chairs. Each product must go through three stages of the manufacturing process: assembly, finishing, and inspection. Each table requires 3 hours of assembly, 2 hours of finishing, and 1.5 hour of inspection. Each chair requires 2 hours of assembly, 2 hours of finishing, and 1 hour of inspection. The profit per table is $150 while the profit per chair is $90. Currently, each week there are 540 hours of assembly time available, 400 hours of finishing time, and 120 hours of inspection time. Linear programming is to be used to develop a production schedule. Define the variables as follows:

Formulate the linear program and determine the number of tables and chairs to produce to maximize profit.

Explanation / Answer

                                      Information Summary

                                           Table                         Chair

Assembly                              3                               2                          540

Finishing                               2                               2                           400

Inspection                            1.5                              1                           120

Let, x & y be the variables which represents the no of tables & chairs to be produced

3x+2y<or equal to 540

2x+2y<or equal to 400

1.5x+1y<or equal to 120

Maximize profit z

z=15x+90y

now,

3x+2y= 540

x=0,y=270

y=0,x=180

2x+2y= 400

x=0,y=200

x=200, y=0

1.5x+1y=120

x=0, y=120

y=0, x=80

solving x=170 y=40

z=15x+90y

The profit will be maximum when tables=200, chairs=200

z=15*200+90*200=18000

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