Question 1098896
your objective function is 40x + 55y


your constraints are:

x >= 20
x <= 60
y >= 10
y <= 40
x + y <= 60


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


therefore you would graph:


x <= 20
x >= 60
y <= 10
y >= 40
x + y >= 60


you would then look for the area of the graph that is NOT shaded.


that would be your region of feasibility.


this is opposite what you would normally do if you were creating the graph manually, or using some software that doesn't have the capability of desmos, the reason being that it is much easier to see the region of feasibility this way when using this software.


if you were creating the graph normaly, or using software that doesn't have the capability of desmos, you would do the following:


you would graph the equality of the constraints and then shade the area of the graph that satisfies them.


in that case, you would graph:


x = 20
x = 60
y = 10
y = 40
x + y = 60


you would then shade the area of the graph that satisfied the constraints by shading the areas of the original inequalities.


those would be, once again:


x >= 20
x <= 60
y >= 10
y <= 40
x + y <= 60


i took the liberty of doing both to show you what each would look like.


with desmos, your graph would look like this:


<img src = "http://theo.x10hosting.com/2017/102501.jpg" alt="$$$" >


using some other sofware (i still used desmos) or creating the graph manually, your graph would look like this:


<img src = "http://theo.x10hosting.com/2017/102502.jpg" alt="$$$" >


in both cases, your objective function with the maximum revenue would be at the corner points of the feasible region.


at (20,40), your profit is 20*40 + 40*55 = 3000
at (20,10), your profit is 20*40 + 10*55 = 1350
at (50,10), your profit is 50*40 + 10*55 = 2550


your maximum profit is when you sell 20 brand A and 40 brand B.


constraints are satisfied because brand A production is between 20 and 60 units and brand B production is between 10 and 40 units.


naturally, minimizing brand A production and maximizing brand B production yields the most profit because the profit of brand B is 15 more than the profit of brand A.