(a) Write the following linear programming problem in standard form.

min 3x1 + 8x2 5x3 + x4

s.t. x1 5x2 + 2x3 x4 1

x1 + 3x3 5

x1 x2 6x3 + x4 = 3

x1, x4 0

x2 0

(b) Give the dual problem for the linear programming problem from part a). [Use the usual dual format, that is, min{b T y : AT y c, y 0}.]

(c) Convert this dual problem into standard form.