Hi, I need some help with these questions. Thanks!

Here are the problems:

1. Put the following LP problem in standard form.

minmize z = 2x(1) + 4X(2) subject to

x(1) + x(3) [greaterorequalto] 4

x(2) + x(3) = 1

x(2), x(3) [greaterorequalto] 0

x(1) unconstrained

I know what to do with the first 3 constraints but what do I do with the x(1) unconstrained variable?

2. Maximize z = 40x(1) + 60x(2) subject to

2(x1) + x(2) [less than or equa lto] 7

x(1) + x(2) [less than or equal to] 4

x(1) + 3x(2) [less than or equal to] 9

x(1), x(2) [greater or equal to] 0

Solve the LP problem using the "corner point" method. Clearly state the optimal value and optimal function.