For a linear programming problem,the objective function is $z = px + qy$,where $p, q > 0$. If at the corner points $(0, 10)$ and $(5, 5)$ the values of $z$ are $90$ and $60$ respectively,then the relation between $p$ and $q$ is . . . . . . .
- A$q = 3p$
- B$p = 3q$
- C$q = 2p$
- D$p = 2q$
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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
View SolutionThe corner points of the feasible region of the objective function $Z = 3x + 9y$ are $(0, 10)$,$(5, 5)$,$(15, 15)$,and $(0, 20)$. Then,the minimum value of $Z$ is:
Let $x$ and $y$ be optimal solutions of a Linear Programming $(LP)$ problem. Then,which of the following is true?
Easy
View SolutionThe corner points of the feasible region are $A(3,3), B(20,3), C(20,10), D(18,12)$ and $E(12, 12)$. The maximum value of $Z=2x+3y$ is $.......$
Medium
View SolutionShow that the minimum of $Z$ occurs at more than two points.
Minimise and Maximise $Z = x + 2y$
subject to $x + 2y \geq 100, 2x - y \leq 0, 2x + y \leq 200; x, y \geq 0$.
Minimise and Maximise $Z = x + 2y$
subject to $x + 2y \geq 100, 2x - y \leq 0, 2x + y \leq 200; x, y \geq 0$.
Medium
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