solve the LP problem

z=5x1 + 2x2

2x1 + 5x2 > 10
4x1 - x2 >12
x1 + x2 >4
x1,x2>0

First question is, do you want to find the max. or min, value of z? You left that out. Secondly, you need to find the solutions to each pair of edge equations for your 3 inequalities. Solve each system:

1. 2x1 + 5x2 = 10 2. 2x1 + 5x2 = 10 3. 4x1 - x2 = 12
4x1 - x2 =12 x1 + x2 = 4 x1 + x2 = 4

Also, plug in the extreme values of 0 for x1 and x2 in turn. When you plug in one, solve for the other. Use those values that are feasible, i.e. > 0 as stated in your conditions. Then test each resulting (x1 , x2) ordered pair in turn in your expression for z. Then whichever one gives it the biggest or lowest value, depending on whether you want to maximize or minimize z, is your result.