CBSE 2024 · Region 1 · Set 2 · Q28 · 3 marks
Solve the following linear programming problem graphically : Maximise $\displaystyle \mathrm{z}=5 \mathrm{x}+4 \mathrm{y}$ subject to the constraints \[\begin{aligned} & \mathrm{x}+2 \mathrm{y} \geq 4 \\ & 3 \mathrm{x}+\mathrm{y} \leq 6 \\ & \mathrm{x}+\mathrm{y} \leq 4 \\ & \mathrm{x}, \mathrm{y} \geq 0 \end{aligned} \]
Marking-scheme solution
Max z = 5x + 4y
Maximum z = $\displaystyle 17$ at x = $\displaystyle 1$, y = $\displaystyle 3$
| Corner Point | Z = 5x + 4y |
| A $\displaystyle (0,2)$ | $\displaystyle 8$ |
| B $\displaystyle (0,4)$ | $\displaystyle 16$ |
| C $\displaystyle (1,3)$ | $\displaystyle 17$ |
| D $\displaystyle \left(\frac{8}{5}, \frac{6}{5}\right)$ | $\displaystyle \frac{64}{5}$ |
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