3. Solve the following linear programming problem. You must usethe dual. First write down the dual maximization LP problem, solvethat, then state the solution to the original minimizationproblem.
(a) Minimize w = 4y1 + 5y2 +7y3
Subject to: y1 + y2 + y3 ≥18
2y1 + y2 + 2y3 ≥ 20
y1 + 2y2 + 3y3 ≥ 25
y1, y2, y3 ≥ 0
(b) Making use of shadow costs, if the 2nd originalconstraint changed to
2y1 + y2 + 2y3 ≥ 24, now whatwill the minimum of w be? Explain clearly.
(c) Making use of shadow costs, if the 1st originalconstraint changed to
y1 + y2 + y3 21, now what willthe minimum of w be? Explain clearly.
