Optimal solution-optimal value and interpret their meanings

Assignment Help Operation Management

Reference no: EM132236200

Maximize 12X1 + 10X2 + 8X3 Total Profit

Subject to X1 + X2 + X3 > 160 At least a total of 160 units of all three products needed

X1 + 3X2 + 2X3 ≤ 450 Resource 1

2X1 + X2 + 2X3 ≤ 300 Resource 2

2X1 + 2X2 + 3X3 ≤ 400 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.

Solution List:

Variable Status Value

X1 Basic 100

X2 Basic 100

X3 NONBasic 0

surplus 1 Basic 40

slack 2 Basic 50

slack 3 NONBasic 0

slack 4 NONBasic 0

Optimal Value (Z) 2200

Linear Programming Results:

X1 X2 X3 RHS Dual

Maximize 12 10 8

Constraint 1 1 1 1 >= 160 0

Constraint 2 1 3 2 <= 450 0

Constraint 3 2 1 2 <= 300 2

Constraint 4 2 2 3 <= 400 4

Solution 100 100 0 2200

Ranging Results:

Variable Value Reduced Cost Original Val Lower Bound Upper Bound

X1 100 0 12 10 20

X2 100 0 10 6 12

X3 0 8 8 -Infinity 16

Dual Value Slack/Surplus Original Val Lower Bound Upper Bound

Constraint 1 0 40 160 -Infinity 200

Constraint 2 0 50 450 400 Infinity

Constraint 3 2 0 300 275 400

Constraint 4 4 0 400 320 420

(a) Determine the optimal solution and the optimal value and interpret their meanings.

(b) Determine the slack (or surplus) value for each constraint and interpret its meaning.

Reference no: EM132236200

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