Question 1141944
When you graph the three inequalities,  
3x + 5y ≥ 20
3x + y ≤ 16
−2x + y ≤ 2

You will get a feasibility region in the shape of a triangle (the triangle is located in Q1 so x>=0 and y>=0 hold).  The corners of the triangle are at:
 (2.8,7.6)
 (5,1)
 (0.769,3.538)

<pre>
Evaluating these (x,y) values in P = 5x + 4y gives:
 (2.8,7.6)       5x + 4y =  44.4      <<< max @ (2.8,7.6)
 (5,1)           5x + 4y =  29
 (0.769,3.538)   5x + 4y =  17.997    <<< min @ (0.769,3.538)


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EDIT:  Added the Desmos graph (picture) below...


*[illustration LPproblem]