Question 1098896: Solve the linear programming problem by using the graphing method illustrated in this example.
A manufacturer of golf clubs makes a profit of $40 per set on a model A set and $55 per set on a model B set. Daily production of the model A clubs is between 20 and 60 sets, inclusive, and that of the model B clubs is between 10 and 40 sets, inclusive. The total daily production is not to exceed 60 sets. How many sets of each model should be manufactured per day to maximize the profit?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! 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:
using some other sofware (i still used desmos) or creating the graph manually, your graph would look like this:
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.
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