Constraint A: $X_{1}+X_{2} \leq 7$ Constraint B: $-2 X_{1}+5 X_{2} \leq 20$
All variables are required to be non-negative. The corner points of the feasible region for this constraint set (assuming the first number in parenthesis is $X_{1}$ and the second number in parenthesis is $X_{2}$ ) are
A) $(0,0),(0,7),(7,0)$
B) $(0,0),(0,4),(7,0)$
C) $(0,0),(0,4),(10,0)$
D) $(0,0),(0,4),(5,2),(10,0)$
E) $(0,0),(0,4),(5,2),(7,0)$

Question

Quizplus · Accepted Answer

The feasible region is determined by the intersection of the constraints, including the non-negativity constraints $X_1 \geq 0$ and $X_2 \geq 0$. By plotting the lines defined by the equations $X_1 + X_2 = 7$, $-2X_1 + 5X_2 = 20$, and considering the axes $X_1 = 0$ and $X_2 = 0$, we find the intersection points that form the boundary of the feasible region. The points (0,0), (0,4), (5,2), and (7,0) are found by solving the system of equations at the intersections of these lines and axes, making option E correct.

Constraint A X1+X2≤7X_{1}+X_{2} \leq 7X1​+X2​≤7 Constraint B −2X1+5X2≤20-2 X_{1}+5 X_{2} \leq 20−2X1​+5X2​≤20

Constraint A $X_{1}+X_{2} \leq 7$ Constraint B $-2 X_{1}+5 X_{2} \leq 20$