1.Consider the following all-integer linear program:

Min 1x₁ + 2x₂ s.t.

C1 1x₁+ 4x₂ < 21

C2 2x₁+ 1x₂ > 7

C3 3x₁+ 1.5x₂ < 21

-2x1 + 6x2>0

x₁, x₂ > 0

a.Graph the constraints for this problem. b.Solve the LP problem and identify the feasible region, corner point solutions, and the optimal solution. c.Suppose the objective function is changed to max 5x1 + 2x2. Find the optimal solution and the value of the objective function. d.Solve the above problem as an integer programming problem (Linear PwP)