SOLUTION: A florist designs two high-profit arrangements— a funeral wreath and a bridal centerpiece. The company’s employees can complete up to 15 arrangements each day using up to 24 to

Let x = # funeral wreath,

    y = # bridal centerpieces.


The profit function (which is the objective function in this problem) is 

    F(x,y) = 60x + 48y  dollars.


The restrictions are

    x + y <= 15        (arrangements)

    4x + y <= 24       (person-hours)

    x >= 0, y >= 0.


The feasible region is shown in the Figure below.


    


    Lines  x + y = 15 (red)  and  4x + y = 24


The feasible region is the quadrilateral in QI, under the green and the red lines.


It has vertices

      P1 = (0,0)

      P2 = (0,15)    y-intercept of red line;

      P3 = (3,12)    intersection of red and green lines

      P4 = (6,0)     x-intercept of green line.


The values of the objective function at the vertices are

      P1 :    F(0,0)   = 60*0 + 48*0 =    0;

      P2 :    F(0,15)  = 60*0 + 48*15 = 720;

      P3 :    F(3,12)  = 60*3 + 48*12 = 756;

      P4 :    F(15,0)  = 60*5 + 48*0  = 300.


The maximum value of the objective function (of the profit) is achieved at point P3.

Hence, this point gives the solution to the problem.


The maximum profit is achieved if the company produces 3 funeral wreath and 12 bridal centerpieces per day.

The maximum profit then is  756 dollars.