Table 8-1
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 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 there are 200 hours of assembly time available,180 hours of finishing time,and 40 hours of inspection time.Linear programming is to be used to develop a production schedule.Define the variables as follows:
T = number of tables produced each week
C = number of chairs produced each week
-According to Table 8-1,which describes a production problem,which of the following would be a necessary constraint in the problem?
A)T + C ≥ 40
B)3T + 2C ≤ 200
C)2T + 2C ≤ 40
D)120T + 80C ≥ 1000
E)None of the above

Question

Quizplus · Accepted Answer

The constraint for assembly time would be 3T + 2C ≤ 200, since each table requires 3 hours of assembly and each chair requires 2 hours of assembly. The constraint for finishing time would be 2T + 2C ≤ 180, since each table requires 2 hours of finishing and each chair requires 2 hours of finishing. The constraint for inspection time would be 1T + 1C ≤ 40, since each table requires 1 hour of inspection and each chair requires 1 hour of inspection. Therefore, the necessary constraint in the problem is 3T + 2C ≤ 200.

Table 8-1 A Small Furniture Manufacturer Produces Tables and Chairs.Each Product Must