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Solve the following linear program graphically: $\begin{array}{ll} \underset{x_1, x_2}{\text{maximize}} & 25 x_1 + 20 x_2\\ \text{subject to} & 3x_1 + 6x_2 \leq 50 \\ & x_1 + 2x_2 \leq 10 \\ & x_1 \geq 0, x_2 \geq 0 \end{array}$

amWhy
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Avijat
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    Have you tried so solve this problem? How far did you get? – Matti P. Feb 15 '23 at 11:41
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    You have posed a problem for others to do but you have not asked a question. What question do you want to ask to help you do this problem? – Paul Feb 15 '23 at 11:46

1 Answers1

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Here, I would like $x$ and $y$ to take rather than $x_1$ and $x_2$. The last sentence says they are both positive, so if we plot this, it is first quadrant. And we plot the above 2 lines in the graph. enter image description here

So we will consider the lower line, there are no intersections between first 2 lines. So we shall check on 2 points $(0,5)$ and $(10,0)$. So putting the values of this points in $25x + 20y$. The answer is (10,0)

Raj Solanki
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