Question

Solve the following linear programming problem graphically:
Maximize : `z=5x+3y`
Subject to:
`x+3yle5`
`x+yle3`
`xge0`
`yge0`

Answer 1

Draw the graph of equations `x+3y=5,x+y=3,x=0` and `y=0`

Now obtain the feasible region for the inequations `x+3yle5,x+yle3,xge0,yge0` and shade it. The convex region is OACB wose vertices are `O(0,0),A(3,0),B(0,5//3)` and `C(2,1)`. Now we will find the value of `z=5x+3y` at each vertex.

Therefore at `x=3,y=0,z` is maximum and its maximum value is 15.