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It's a linear programming problem.We have to maximise the value of p=2x+3y.
Subject to 2x+y<= 15
x>=0 and y>=0
So first of all we will draw the inequality graph of the linear equation. The corner point or the point where the equation meets will give the maximum value of x and y of the expression.
Considering equality draw the graph of 2x+y=15
Table of values
Using these pair (0,15)(7,1) draw the line.
Region :Below the line as when x=0,y<=15 So all values less than 15 or the region below the line.
For the x+3y=20
Draw the line similarly using th above coordinate pair.The region will be below the line.
Also x>=0 and y>=0 is the 1st quadrant.
Drawing the graph.
From the graph ,the corner point is x=5 and y=5 and the maximum value of p=2*5+3*5=10+15=25(answer)
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