Thread: Algebra Maximizing Function

Maximize the function P=2x+3y

with the following constraints:

X is greater than or equal to 0
0 is less than or equal to y is less than or equal to 1
3x+y is less than or equal to 3

Let's write the conditions.



And we want to maximize:

We have to maximize both x and y to get a maximum 2x + 3y.
As and we want to maximize x and y, making it less than 3 won't make x and y maximum. So,

x can be any positive integer but y is between (or equal to) 0 and 1. This means finding y is better cuz when we use y, we don't have to think of x, as it can be any positive integer.




Then,



The greater y will make our P bigger. But we have a condition for y, . The greatest y value we can use is 1. For y=1, x is 2/3. So P is .

Hello, neoseeker191!

Maximize the function: .
with the following constraints: .

This is a Linear Programming problem.
You should have been shown the approach by now . . .

Graph the inequalities; shade the appropriate regions.
Determine the vertices of the resulting polygon.
Test the vertices (coordinates) in the given function.

The graph should look like this:

Code:

        |
      3 |
        |\
        | \
        |  \
        |   \
        |    \
      1 o - - o - -
        |::::::\
        |:::::::\
        |::::::::\
      - o - - - - o - -
        |         1\

Determine the four vertices.
You should get: .

Now see which one produces maximum