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Mathematics · 2024 · 3 marks
Linear ProgrammingLinear Programming Problem and its Mathematical Formulation3 marksApplyshort answer
CBSE 2024 · Region 1 · Set 3 · Q26
Solve the following linear programming problem graphically: Minimise z =5 x -2 y subject to the constraints x +2 y ≤ 120; x + y ≥ 60; x -2 y ≥ 0; x,…
Solve the following linear programming problem graphically : Minimise $\displaystyle \mathrm{z}=5 \mathrm{x}-2 \mathrm{y}$ subject to the constraints \[\begin{aligned} & \mathrm{x}+2 \mathrm{y} \leq 120 \\ & \mathrm{x}+\mathrm{y} \geq 60 \\ & \mathrm{x}-2 \mathrm{y} \geq 0 \\ & \mathrm{x}, \mathrm{y} \geq 0 \end{aligned} \]
Marking-scheme solution
Min $\displaystyle \mathrm{z}=5 \mathrm{x}-2 \mathrm{y}$
$\displaystyle \operatorname{Min} \mathbf{Z}=160$ at $\displaystyle \mathrm{x}=40, \mathrm{y}=20$
| Corner Points | $\displaystyle \mathrm{Z}=5 \mathrm{x}-2 \mathrm{y}$ |
| $\displaystyle \mathrm{A}(60,0)$ | $\displaystyle 300$ |
| $\displaystyle \mathrm{~B}(40,20)$ | $\displaystyle 160$ |
| $\displaystyle \mathrm{C}(60,30)$ | $\displaystyle 240$ |
| $\displaystyle \mathrm{D}(120,0)$ | $\displaystyle 600$ |
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