Thank you for the opportunity to help you with your question!

It's a linear programming problem.We have to maximise the value of p=2x+3y.

Subject to 2x+y<= 15

x+3y<=20

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

x y

0 15

7 1

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

Table of values

x y

2 6

5 5

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)

Please let me know if you need any clarification. I'm always happy to answer your questions.

Oct 26th, 2015

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