Consider the following linear programming model:
$$\begin{array} { l l }
\operatorname { Min } & 2 \mathrm { X } _ { 1 } + 3 \mathrm { X } _ { 2 } \
\text { Subject to: } \
& \mathrm { X } _ { 1 } + 2 \mathrm { X } _ { 2 } \leq 1 \
& \mathrm { X } _ { 2 } \leq 1 \
& \mathrm { X } _ { 1 } \geq 0 , \mathrm { X } _ { 2 } \leq 0
\end{array}$$
This problem violates which of the following assumptions?
A)additivity
B)divisibility
C)non-negativity
D)proportionality
E)linearity

Question

Consider the following linear programming model:
$$\begin{array} { l l } 
\operatorname { Min } & 2 \mathrm { X } _ { 1 } + 3 \mathrm { X } _ { 2 } \
\text { Subject to: } \
& \mathrm { X } _ { 1 } + 2 \mathrm { X } _ { 2 } \leq 1 \
& \mathrm { X } _ { 2 } \leq 1 \
& \mathrm { X } _ { 1 } \geq 0 , \mathrm { X } _ { 2 } \leq 0
\end{array}$$
This problem violates which of the following assumptions?
A)additivity
B)divisibility
C)non-negativity
D)proportionality
E)linearity

Quizplus · Accepted Answer

The problem violates the non-negativity assumption. The constraint $\mathrm{X}_2\leq1$ implies that $\mathrm{X}_2$ is non-negative, which contradicts the assumption that $\mathrm{X}_2\leq0$.

Consider the Following Linear Programming Model This Problem Violates Which of the Following Assumptions? A)additivity B)divisibility

Consider the Following Linear Programming Model This Problem Violates Which of the Following Assumptions?
A)additivity
B)divisibility