SOLUTION
From the what is given
[tex]\begin{gathered} x+y\le5 \\ x\ge3 \\ 2y\le8 \\ x\ge0 \\ y\ge0 \end{gathered}[/tex]
We have the graph as shown below
We are told that the MAX is
[tex]5x+2y[/tex]
Substituting these required points into the equation, our maximum becomes
[tex]\begin{gathered} 5x+2y \\ \text{For (3, 2)} \\ 5(3)+2(2)=15+4=19 \\ \text{For }(3,\text{ 0)} \\ 5(3)+2(0)=15+0=15 \\ \text{For (5, 0)} \\ 5(5)+2(0)=25+0=25 \end{gathered}[/tex]
We can see that the maximum is 25 at for units of 5, that is x = 5
But we are told in (B) that
[tex]x\ge3[/tex]
Hence the surplus unit is
[tex]5-3=2[/tex]
Hence the answer is 2
