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

Question

26.

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: X = number of tables produced each week, and Y = number of chairs of produced each week.

Suppose it is decided that the number of hours used in the inspection process must be at most 80 percent of the number of hours used in the finishing department. How would this constraint be written?

Select one:

a. 0.6X + 0.6Y 0.80

b. -06X - 0.6Y 0.80

c. 0.6X + 0.6Y 0.20

d. 0.6X - 0.6Y 0.80

e. -0.6X - 0.6Y 0

Explanation / Answer

Let the number of tables and chairs produced per weekare x and y respectively. Then the time reqired gor inspection is 3x +2y = 200; the time required for finishing is 2x+2y = 180 and the time required for inspection is x +y = 40.

Also P(x), the profit per week is 120x +80y .

If the number of hours used in the inspection process must be at most 80 % of the number of hours used in finishing, then x+y 0.8(2 x+2y ) or, x+y   1.6x +1.6y or, - 0.6x - 0.6y   0.

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