Question

# A furniture company produces tables (X) and chairs (Y). Available resources have indicated that the production...

A furniture company produces tables (X) and chairs (Y). Available resources have indicated that the production volume level should not exceed 1200 units per week and the demand for chairs is at most half of that for tables. Further, the production level of tables can exceed three times the production of chairs by at most 600 units. If the company makes a profit of OMR12 and OMR 16 per unit respectively on tables and chairs, how many of each should be produced weekly in order to maximize the profit.

which of the following represents one of the constraints for the above business problem

Let no of Tables be (X1) and no chairs are (X2).

We have the objective function as 12X1 + 16 X2 = Z = Maximize

We have three constraints as follows:

X1 + X2 < = 1200 ( Production volume level constraint)

X2 < = X1 / 2 or 2X2 <= X1 or - X1 + 2X2 < = 0 ( Demand constraint)

X1 - 3X2 <=600 ( Production level constraint)

By graphical method we have X1= 800 and X2 = 400 and value of Z is 16000.

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