Question

A company produces two products: X1and X2. The profit per unit of product is $250 for X1 and $550 for X2. The company has developed a linear programming model to maximize profit for next month and has run it on QM for Windows. The following is the QM Ranging report.(The company has already paid for all resources that are required in the mode.)

Variable    Value    Reduced Cost    Original Val Lower Bound    Upper Bound
X1             400              0                 250          0                       275
X2               400              0                 550          500                   Infinity

                Dual Value Slack/Surplus     Original Val     Lower Bound      Upper Bound
Constraint 1    0             1600             7200             5600             Infinity
Constraint 2    0             1000               3000             2000             Infinity
Constraint 3   275             0                  1200             400               1600
Constraint 4    -25             0                  400                0                  1200

Constraint 5     0             200                600              400              Infinity

The objective function is to maximize:

1. Z = $400X1 + $400X2

2. Z = $250X1 + $550X2

3. Z=$275X1

4. Z = $500X2

5. None of the above

Answer 1

Here, objective of the company is to maximize the profit. Profit on product X1 = $250 per unit and product X2 is $550 per unit. So, the objective functions is to maximize:

Z = $250X1 + $550X2