SOLUTION: The ACME company makes two types of rings: the VIP and the SST. They can produce up to 24 rings every day using up to 60 total man-hours. It takes 3 man-hours to make one VIP rin

Let  X = # of the VIP rings, and

     Y = # of the SST rings.


Then the problem is to maximize the objective (=the profit) function  

    P(X,Y) = 40X + 35Y

under these restrictions

    X + Y <= 24,

    3X + 2Y <= 60,

    X >= 0,  Y >= 0.


The feasibility domain is shown at the plot below.


    


    Plot X + y = 24 red),  3x + 2y = 60 (green)



It is the quadrilateral in QI under the red and green lines.


Corner points are  

     P1 = (0,24)     (red line y-interception);

     P2 = (12,12)    (intersection the red and the green lines);

     P3 = (20,0)     (green line x-interception).


Calculate the profit function at the corner points


     P1:  P(0,24)  = 40*0  + 35*24 = 840;

     P2:  P(12,12) = 40*12 + 35*12 = 900;

     P3:  P(20,0)  = 40*20 + 35*0  = 800.


The maximum value is at P2.

Hence, the solution is the point P2 with  X= 12 (the number of the VIP rings)  and  Y = 12 (the number of the SST rings)  

                       and the profit value of  900 dollars.    ANSWER