Question: Answer Questions 2 and 3 based on the following LP problem.

Maximize 6X1 + 5X2 + 4X3 Total Profit

Subject to X1 + X2 + X3 > 220 At least a total of 220 units of all three products needed

X1 + 3X2 + 2X3 ≤ 500 Resource 1

2X1 + X2 + 2X3 ≤ 350 Resource 2

3X1 + 2X2 + 3X3 ≤ 600 Resource 3

And X1, X2, X3 ≥ 0

Where X1, X2, and X3 represent the number of units of Product 1, Product 2, and Product 3 to be manufactured.

The QM for Windows output for this problem is given below.

Original problem with Answers:

X1 X2 X3 RHS Dual

Maximize 6 5 4

Constraint 1 1 1 1 >= 220 0

Constraint 2 1 3 2 <= 500 0.8

Constraint 3 2 1 2 <= 350 2.6

Constraint 4 3 2 3 <= 600 0

Solution-> 110 130 0 Optimal Z-> 1310

Linear Programming Results:

Variable Status Value

X1 Basic 110

X2 Basic 130

X3 NONBasic 0

surplus 1 Basic 20

slack 2 NONBasic 0

slack 3 NONBasic 0

slack 4 Basic 10

Optimal Value (Z) 1310

Ranging Results:

Variable Value Reduced Cost Original Val Lower Bound Upper Bound

X1 110 0 6 2.5 10

X2 130 0 5 3 18

X3 0 2.8 4 -Infinity 6.8

Constraint Dual Value Slack/Surplus Original Val Lower Bound Upper Bound

Constraint 1 0 20 220 -Infinity 240

Constraint 2 .8 0 500 400 550

Constraint 3 2.6 0 350 300 357.1429

Constraint 4 0 10 600 590 Infinity

1. Determine the optimal solution and optimal value and interpret their meanings.
2. Determine the slack (or surplus) value for each constraint and interpret its meaning.

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