Question 1166880
the graphical solution is shown below.


<img src = "http://theo.x10hosting.com/2020/100903.jpg" >


your variables are:


x = number of gallons of new rhythm.
y = number of gallons of crown alternate


your objective function is:


p = 2.5 * x + 4.0 * y


your constraints functions are:


x >= 30,000
y >= 15,000
x <= 80,000
y <= 40,000
.02 * x + .01 * y <= 2,000
.03 * x + .05 * y <= 2,500


using the desmos.com calculator, you would graph the OPPOSITE of these inequalities.


specifically, you would graph:


x <= 30,000
y <= 15,000
x >= 80,000
y >= 40,000
.02 * x + .01 * y >= 2,000
.03 * x + .05 * y >= 2,500


the feasible region on the graph is the area of the graph that is NOT shaded.


your max / min solution will be at the corner points of the feasible region.


you will evaluate your objective function at each of these corner points, using the value of x and the value of y shown in the format of (x,y) on the graph.


the following table shows the points and the value of the objective function as those points.


<pre>

x                  y                   2.5 * x + 4.0 * y

30,000             32,000              203,000
30,000             15,000              135,000
58,333.333         15,000              205,833.3325

</pre>


the results show the maximum profit is attained when x = 58,333.333 and y = 15,000.


this means 58,333.333 gallons of new rhythm and 15,000 gallons of crown alternate are produced and sold.


all the constraints have to be satisfied as well.


when x = 58,333.333 and y = 15,000, .....


x >= 30,000 is satisfied.
y >= 15,000 is satisfied.
x <= 80,000 is satisfied.
y <= 40,000 is satisfied.
.02 * x + .01 * y = 1316.667 under 2000 is satisfied.
.03 * x + .05 * y = 2500 under 2500 is satisfied.


all the constraints are satisfied, therefore the maximum profit solution is confirmed to be good, based on the graphical analysis.