(Solved Homework): Operations reasearch class Identify the direction of decrease…

Operations reasearch class

Identify the direction of decrease in z in each of the following cases:

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a. Minimize z = 4×1 – 2×2

b. Minimize z = -3×1 + x2

c. Minimize z = -x1 – 2×2

I do not understand how to find the direction. I have figured out what z is and how to graph it but not which direction to point the arrow.

Expert Answer

We can follow the simple rule as –

Note the coefficients of the objective.
- If both are negative, draw the objective line in the 3rd quadrant
- If coefficient of x1 is (-)ve but that of the x2 is (+)ve, draw it is 2nd quadrant
- If coefficient of x1 is (+)ve but that of the x2 is (-)ve, draw it is 4th quadrant
- If both are positive, draw the objective line in the 1st quadrant
Then move the objective line towards the origin – that’s the direction

(a)

z = 4×1 – 2×2; The coefficient of x1 is (+)ve but that of the x2 is (-)ve, so, draw it is 4th quadrant and move towards the origin.

(b)

z = -3×1 + x2; The coefficient of x1 is (-)ve but that of the x2 is (+)ve, so, draw it is 2nd quadrant and move towards the origin.

(c)

z = -x1 – 2×2, Here, both the coefficients are negative so, draw the objective line in the 3rd quadrant.

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