Using the following system of inequalities find the maximum value of f(x,y) = 3x + 9y x=0 y=0 3x+2y=18 6x+7y=42

Question

Using the following system of inequalities find the maximum value of f(x,y) = 3x + 9y
x≥0
y≥0
3x+2y≤18
6x+7y≤42

Answer 1

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Answer 2

Star,

 

This is a linear programming problem. What you must do it graph each inequality on a single set of axes, find the coordinates of ALL corner points of the shaded region, plug them into the function f(x,y), then choose the largest value for the maximum.

 

I cannot draw the region here, but here are the coordinates of the vertices (corners):

 

(0,0), (6,0), (14/3,2), and (0,6)

 

If you need help finding these, I suggest you send a reply back to me and I will provide more details.

 

When you plug these into the function f(x,y) = 3x + 9y, you obtain the following values:

 

f(0,0) = 0

f(6,0) = 18

f(14/3,2) = 32

f(0,6) = 54

 

Looking at these numbers, you can see that the maximum value of f subject to these constraints is 54.

 

Let me know if you need more explanation on how to find the vertices. It takes a lot of typing to explain this all at once, so I will leave it to you to ask for more help.