SOLUTION: Evan runs a factory that makes Blu-ray players. Each T50 takes 4 ounces of plastic and 4 ounces of metal. Each G150 requires 2 ounces of plastic and 6 ounces of metal. The factory

Let X = # of items T50;  Y = # of items G150.


From the condition, we have this formulation of maximization problem:


    (1)  the objective function to maximize is the profit  P = 12X + 11Y  dollars.


Restrictions


    (2)  4X + 2Y <=  140            (plastic restriction)

    (3)  4X + 6Y <=  324            (metal restriction)

    (4)   0 <= X <= 16,  Y >= 0.


You can make a plot of the feasibility domain.


    


    Plots y =   (red);  y =  (green);  x = 16 (blue)



It is a pentagon in QI adjacent to x- and y-axes, restricted by the red, the green and the blue lines.


It has vertices (X,Y) = (0,0), (0,54), (12,46), (16,38), (16,0).


The solution is one of these 5 points, where the objective function (profit) has a maximum.


The values of the function  P(X,Y)  at listed points are


    P(0,0)                      =   0,

    P(0,54)   = 12*0  + 11*54   = 594,

    P(12,46)  = 12*12 + 11*46   = 650,

    P(16,38)  = 12*16 + 11*38   = 610,

    P(16,0)   = 12*16  + 11*0   = 192.


Comparing these values, you find the optimal point.

It is  (X,Y) = (12,46),  12 items T50 and 46 items G150, providing maximum profit of 650 dollars.     ANSWER