Question

Suppose that the first goal in a GP problem is to make 3 X1 + 4 X2 approximately equal to 36. Using the deviational variables d1− and d1+, the following constraint can be used to express this goal.​
3 X1 + 4 X2 + d1− − d1+ = 36

If we obtain a solution where X1 = 6 and X2 = 2, what values do the deviational variables assume?

a. d1− = 0, d1+ = 10
b. d1− = 6, d1+ = 0
c. d1− = 5, d1+ = 5
d. d1− = 10, d1+ = 0

Answer 1

Answer:

d. d1− = 10, d1+ = 0

Explanation:

Given

3X1 + 4X2 +d1− − d1+ = 36

X1 = 6

X2 = 2

Required

Possible values of d1- and d1+

We have:

3X1 + 4X2 +d1− − d1+ = 36

Substitute values for X1 and X2

3 *6 + 4 * 2 + d1- - d1+ = 36

18 + 8 + d1- - d1+ = 36

Collect like terms

d1- - d1+ = 36 - 18 - 8

d1- - d1+ = 10

For the above equation to be true, the following inequality must be true

d1- > d1+

Hence,

(d) is correct

Because:

10 > 0