Problem 2) Minimize M2 (1) subject to 2M1 – M2 +320 (2) M1 + M2 2 2 (3) M2 2 M1 20 (4) a) Apply the NC and SC and check the constraints. b) Show the feasible region (plot). c) Find the minimum M2 using the inequality constraint method.

Sketch the region corresponding to the system of constraints. Then find the minimum and maximum values of the objective function z=3x+2y and the points where they occur, subject to the constraints. x+4y202x+y12x0y0

Use your schools library, the Internet, or some other reference source to find the real-life applications of constrained optimization.

A company manufactures  x number of  top load washing machines and y number of front loading machines . The objective function is the profit function         P= 20x+25y If on graphing the constraints and finding the feasible region, the vertices are   (2,5)   (13,5)  (16,2)  (2,2)   A) Determine the maximum profit. B)How many top load machines should be made to maximize profit? C)How many front load machines should be made to maximize profit?