If an $LPP$ admits an optimal solution at two consecutive vertices of a feasible region,then:
- Athe required optimal solution is at the midpoint of the line joining two points.
- Bthe optimal solution occurs at every point on the line joining these two points.
- Cthe $LPP$ under consideration is not solvable.
- Dthe $LPP$ under consideration must be reconstructed.
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The corner points of the feasible region determined by the system of linear inequalities $2x + y \leq 10$,$x + 3y \leq 15$,$x, y \geq 0$ are $(0,0)$,$(5,0)$,$(3,4)$,and $(0,5)$. Let $Z = qx + py$ where $p, q > 0$. The condition on $p$ and $q$ such that the maximum of $Z$ occurs at both $(3,4)$ and $(0,5)$ is:
The corner points of the feasible region determined by the following system of linear inequalities: $2x + y \leq 10$,$x + 3y \leq 15$,$x, y \geq 0$ are $(0,0)$,$(5,0)$,$(3,4)$,and $(0,5)$. Let $Z = px + qy$,where $p, q > 0$. The condition on $p$ and $q$ so that the maximum of $Z$ occurs at both $(3,4)$ and $(0,5)$ is:
Medium
View SolutionThe minimum value of $Z = 2x + 3y$ for the system of linear constraints: $2x + 4y \leq 12$,$x + y \leq 3$,$x \geq 0$,and $y \geq 0$ is . . . . . . .
The constraints $-x_{1} + x_{2} \leq 1$,$-x_{1} + 3x_{2} \leq 9$,and $x_{1}, x_{2} \geq 0$ define:
For the $LP$ problem,minimize $z = 2x + 3y$,the coordinates of the corner points of the bounded feasible region are $A(3, 3), B(20, 3), C(20, 10), D(18, 12),$ and $E(12, 12)$. The minimum value of $z$ is:
Medium
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