Determine graphically the minimum value of the objective function `Z=-50 x+20 y` subject to the constraints: `2x-ygeq-5` , `3x+ygeq3` , `2x-3ylt=12` , `xgeq0,""""ygeq0`.

Explanation

Given objective function is `Z=−50x+20y`
We have to minimize Z on given constraints
`2x−y>=−5`
`3x+y>=3` ,
`2x−3y<=12`
`x>=0,y>=0`
After plotting all the constraints we get the common region (Feasible region) as shown in the image.
There are four corner points `(0,5)`,`(0,3)`,`(1,0)` and `(6,0)`
Now, at corner points value of Z are as follows :
`[["Corner point",|,Z=-50x+20y],[A=(0,5),|,100],[B=(0,5),|,60],[C=(1,0),|,-50],[D=(6,0),|,-300]]`
Since common region is unbounded. So, value of Z may be minimum at `(6,0)` and minimum value may be `-300.`
Now to check if this minimum is correct or not, we have to draw region `−50x+20y<=−300`
Since, there are some common region with feasible region(See image). So, `-300` will not be minimum value of Z.
Hence, Z has no minimum value.