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

Question

A small furniture manufacturer produces tables and chairs.Each product must gothrough three stages of the manufacturing process—assembly, finishing, and inspection.Each table requires 3 hours of assembly, 2 hours of finishing, and 1 hour of inspection.Each chair requires 2 hours of assembly, 2 hours of finishing, and 1 hour of inspection.The profit per table is $120 while the profit per chair is $80.Currently, each week thereare 200 hours of assembly time available, 180 hours of finishing time, and 40 hours ofinspection time.Linear programming is to be used to develop a production schedule.Define the variables as follows:T = number of tables produced each weekC = number of chairs produced each week

1- According to Table 8.2, which describes a production problem, suppose it is decided that the number of hours used in the assembly process must be at least 80 percent of the time available. How would this constraint be written?

none of these


2-

3T + 2C 160

3T + 2C 200

3T + 2C 200

3T + 2C 160

none of these


2-

Explanation / Answer

T = number of tables produced each week

C = number of chairs produced each week

Ojective function

To maximize profit z= 120T + 80C

subjected to constraints

3T + 2C <= 200 (for assembly constraint)

2T + 2C <= 180 (for finishing constraint)

T + C < = 40 (inspection constraint)

given it is decided that the number of hours used in the assembly process must be at least 80 percent of the time available

3T + 2C >=200*.8

3T + 2C >=160

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