Constraints in Linear Programming

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Scenario: 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 Exhibit 8-1, which describes a production problem, which of the following would be a necessary constraint in the problem?

a. T + C < 180
b. 120T + 80C > 1000
c. T + C < 200
d. T + C < 40
e. none of the above

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