The objective function for a LP model is 3 X 1 + 2 X 2. If X 1 = 20 and X 2 = 30, what is the value of the objective function?

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BlackTom AI · Accepted Answer

To begin, let's restate the problem in our own words and identify what we are computing: the objective function is 3X1 + 2X2, and the given values are X1 = 20 and X2 = 30. We need to plug these numbers into the function.

Option 1: 60. This would correspond to a calculation like 3*20 = 60, or perhaps 2*30 = 60, but it ignores the contribution from the other variable. Since both terms in the objective function contribute, this result is incomplete.

Option 2: 50. This value does not align with the actual arithmetic of 3*20 + 2*30. If you attempt to compute 3*20 = 60 and 2*30 = 60, adding them yields 120, not 50. Thus this is incorrect.

Option 3: 0. A zero objective value would imply that both terms vanish, which would require X1 = 0 and X2 = 0. Since X1 and X2 are given as 20 and 30, this option contradicts the data and is not feasible.

Option 4: 120. This is the correct computation: 3 times X1 (3*20 = 60) plus 2 times X2 (2*30 = 60) sums to 120. This matches the standard evaluation of a linear objective function at the specified point.

In summary, the only option that aligns with straightforward substitution into the objective function is 120, because both components contribute positively: 60 from 3*X1 and 60 from 2*X2, totaling 120. The other options ignore one or both terms or miscalculate the underlying arithmetic, leading to incorrect results.

BU.520.601.T2.FA25 Final Exam

The objective function for a LP model is 3 X 1 + 2 X 2. If X 1 = 20 and X 2 = 30, what is the value of the objective function?

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