Solve the following linear programming problem graphically:
Minimize: `z=x+3y`
Subject to:
`x+yle8`
`3x+5yge15`
`xge0`
`yge0`

Explanation

Draw the graph of equations `x+y=8, 3x+5y=15,x=0` and `y=0`.
Now obtain the feasible region for he inequalities `x+yle8, 3x+5yge15 xge0` and `yge0`. The convex region is ABCD whose vertices are `A(8,0), B(0,8),C(0,3)` and `D(5,0)`. Now we will find the value of `z=x+3y` at each vertex.

Therefore at `x=5` and `y=0,z` is minimum and minimum value is 5.