SOLUTION: An appliance store sells two types of refrigerators. Each Cool-It refrigerator sells for $640 and each Polar sells for $780. Up to 250 refrigerators can be stored in the warehouse

Algebra ->  Equations -> SOLUTION: An appliance store sells two types of refrigerators. Each Cool-It refrigerator sells for $640 and each Polar sells for $780. Up to 250 refrigerators can be stored in the warehouse       Log On


   

Question 1097217: An appliance store sells two types of refrigerators. Each Cool-It refrigerator sells for $640 and each Polar sells for $780. Up to 250 refrigerators can be stored in the warehouse and new refrigerators are delivered only once a month. It is known that customers will buy at least 80 Cool-Its and at least 120 Polars each month. How many of each brand should the store stock and sell each month to maximize revenues?
Answer by ikleyn(52781) About Me  (Show Source):
You can put this solution on YOUR website!
.
Let X be the number of $640-refrigerators 
and Y be the number of $780-refrigerators.


Then the Revenue function is  R(X,Y) = 640*X + 780*Y.    (1)


The constraints are 

X + Y <= 250,     (2)  

X >= 80           (3)

Y >= 120.         (4)


The feasible domain is the triangle in the first quadrant coordinate (X,Y)-plane restricted by the straight lines (2), (3) band (4).

The vertices of this triangle are   (MAKE YOUR SKETCH !)

    P1 = (80, 120),
    P2 = (80, 170),    ( <<<---===   notice that 80  + 170 = 250 ! )
    P3 = (130,120)     ( <<<---===   notice that 130 + 120 = 250 ! )


You need to maximize the function (1) over this triangle.


Apply the linear programming method.
The method says: 

    To find the maximum, calculate the function F(X,Y) at the vertices of the polygon (at the vertices of the triangle, in this case !)

    and select that vertex where the function is maximal.


So,  at  P1:  F( 80,120) =  80*640 + 120*780 = 144800;

     at  P2:  F( 80,170) =  80*640 + 170*780 = 183800;

     at  P3:  F(130,120) = 130*640 + 120*780 = 176800.


As you see, the function F(X,Y) is maximal at P2.

Hence,  X = 80  and  Y = 170 is the optimal solution.


Answer.  80 $640 refrigerators and 170 $780 refrigerators provide the maximal revenue of $183800.