In XYZ Inc. the goal for labor utilization is 500 hours per month, and the firm is making two products$\mathrm{X}_{1}$ and $\mathrm{X}_{2}$, which denote the units of these products produced per month. $\mathrm{X}_{1}$ requires 3 hours per unit for labor, and $\mathrm{X}_{2}$ requires 5 hours per unit for labor. The corresponding goal programming constraint would be
A) $3 X_{1}+5 X_{2}=500$
B) $3 X_{1}+5 X_{2} \leq 500$
C) $3 \mathrm{X}_{1}+5 \mathrm{X}_{2}+\mathrm{u}_{1}-\mathrm{v}_{1} \leq$500
D) $3 \mathrm{X}_{1}+5 \mathrm{X}_{2}+\mathrm{u}_{1}-\mathrm{v}_{1}=$ 500

Question

Quizplus · Accepted Answer

In goal programming, the objective is to meet the target as closely as possible, which can involve either underachievement or overachievement of the target. The terms $u_1$ and $v_1$ represent the deviation variables for underachievement and overachievement, respectively. Thus, the equation $3X_1 + 5X_2 + u_1 - v_1 = 500$ correctly represents the goal programming constraint for achieving a labor utilization goal of 500 hours, taking into account both possible underachievement and overachievement of this goal.

In XYZ Inc X1\mathrm{X}_{1}X1​ And X2\mathrm{X}_{2}X2​ , Which Denote the Units of These Products Produced Per

In XYZ Inc $\mathrm{X}_{1}$ And $\mathrm{X}_{2}$ , Which Denote the Units of These Products Produced Per