Question

Solve the following LP formulation and determine the number of Surplus units in constraint B.

Answer 1

From the what is given

`\begin{gathered} x+y\le5 \\ x\ge3 \\ 2y\le8 \\ x\ge0 \\ y\ge0 \end{gathered}`

We have the graph as shown below

We are told that the MAX is

`5x+2y`

Substituting these required points into the equation, our maximum becomes

`\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}`

We can see that the maximum is 25 at for units of 5, that is x = 5

But we are told in (B) that

`x\ge3`

Hence the surplus unit is

`5-3=2`

Hence the answer is 2