Question 1162265
x = number of acres of corn.
y = number of acres of soybeans.


make a table as shown below:


<pre>
                             x                   y
                           corn              soybeans

fertilizer gallons           7                   3         <= 40,500
harvest hours                .5                  1         <= 5,250
profit                       50                  45        maximize
</pre>


using the desmos.com calculator, graph the opposite of the constraints and then evaluate the objective function at the corner points of the feasible region.


the constraint functions are:


7x + 3y <= 40,500
.5x + y <= 5250
x,y >= 0


the objective function is:


profit = 50x + 45y


you are graphing the OPPOSITE of the constraint inequalities.


here's what the graph looks like:


<img src = "http://theo.x10hosting.com/2020/071301.jpg" >


maximum profit is at the point (4500,3000).
profit is 50*4500 + 45*3000 = 360,000
gallons of fertilizer used are 4500*7 + 3000*3 = 40,500 <= 40,500
hours of labor = 4500*.5 + 3000*1 = 5250 <= 5250


looks like all the available resources were used when the maximum profit was attained.