Question 1171978
set up a table as shown beloow:
<pre>
                              x                   y
                      air conditioner            fan

wiring                        6                   1           <= 240
drilling                      2                   1           <= 77
profit                        25                  15          maximize

</pre>


your objective function is 25x + 15y.
this is what you want to maximize.


your constraint functions are:
6x + y <= 240
2x + y <= 77
x >= 0
y >= 0


using the desmos.com calculator, you will graph the opposite of the contsraint functions.
the area on the graph that is not shaded is your region of feasibiliy.
your maximum profit will be at the corner points of the feasible region.
you find the maximum profit by evaluating the objective function at each of the corner points.


the graph looks like this.


<img src = "http://theo.x10hosting.com/2020/122601.jpg" >


total profit is shown below with all constraints met.


<pre>
x	y	drill	wire	profit
0	77	154	77	1155
21.5	55.5	240	77	1370
40	0	240	40	1000
</pre>


total drill hours are less than or equal to 240
total wire hours are less than or equal to 77
maximum total profit is 1370 when x = 21.5 and y = 55.5