Consider the following constraint: 2x1 + 3x2 =60. Assume that we convert this constraint into a goal constraint with the value of x1 = 15 and the value of x2 = 15. Then the values of d1+ and d1- are ________ and ________, respectively.
A) 0, 15
B) 15, 0
C) 20, 0
D) 0, 20

Question

Quizplus · Accepted Answer

Using x1=15 and x2=15 in the constraint, we get:
2(15) + 3(15) = 60
Therefore, the constraint is satisfied.
For the goal constraint, we need to find the range of values for which the constraint remains satisfied given the values of x1 and x2.

d1+ represents the maximum increase in the left-hand side of the constraint (i.e. maximum increase in the value of 2x1 + 3x2) that is possible while still keeping x1=15 and x2=15.

d1- represents the maximum decrease in the left-hand side of the constraint (i.e. maximum decrease in the value of 2x1 + 3x2) that is possible while still keeping x1=15 and x2=15.

To find d1+, we can increase the value of x1 while keeping x2=15 such that the constraint still remains satisfied. Since the coefficient of x1 is 2, we can increase x1 by 1 unit to get:

2(16) + 3(15) = 63

This is the maximum increase possible while still keeping x1=15 and x2=15. Therefore, d1+ = 3.

To find d1-, we can decrease the value of x1 while keeping x2=15 such that the constraint still remains satisfied. Since the coefficient of x1 is 2, we can decrease x1 by 1 unit to get:

2(14) + 3(15) = 57

This is the maximum decrease possible while still keeping x1=15 and x2=15. Therefore, d1- = 3.

Hence, the answer is B) 15, 0.

Consider the Following Constraint: 2x1 + 3x2 =60