Question 1134444
.
<pre>
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.


    {{{graph( 330, 330, -5, 30, -5, 30,
          24-x, (60-3x)/2
)}}}


    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.    <U>ANSWER</U>
</pre>

Solved.


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To see other similar problems solved by the Linear Programming method, &nbsp;look into the lesson

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/word/misc/Solving-minimax-problems-by--the-Linear-Programming-method.lesson>Solving minimax problems by the Linear Programming method</A> 

in this site.


Also, &nbsp;look into the solutions of other similar problems in the archive to this forum under the links


https://www.algebra.com/algebra/homework/Graphs/Graphs.faq.question.1131906.html

https://www.algebra.com/algebra/homework/coordinate/word/Linear_Equations_And_Systems_Word_Problems.faq.question.1131043.html

https://www.algebra.com/algebra/homework/word/finance/Money_Word_Problems.faq.question.1129285.html

https://www.algebra.com/algebra/homework/Finance/Finance.faq.question.1128383.html

https://www.algebra.com/algebra/homework/Linear-equations/Linear-equations.faq.question.1123217.html

https://www.algebra.com/algebra/homework/Finance/Finance.faq.question.1102103.html


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