SOLUTION: I am definitely confused and can't understand, if you can please explain in detailed steps, I keep going round in circles and my steps are taking forever I need to rewrite the c

Algebra ->  College  -> Linear Algebra -> SOLUTION: I am definitely confused and can't understand, if you can please explain in detailed steps, I keep going round in circles and my steps are taking forever I need to rewrite the c      Log On


   

Question 932521: I am definitely confused and can't understand, if you can please explain in detailed steps, I keep going round in circles and my steps are taking forever
I need to rewrite the constraints in slope intercept,
List all vertices of the feasible region as ordered pairs,
list values of the objective function for each vertex,
list maximum or minimum amount, including x and y value
3x+5y >= 35
2x + y <= 14
x >= 0, y>= 0
Maximum for P= 3x + 2y
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Slope intercept form is y=mx%2Bb
3x%2B5y%3E=35
5y%3E=-3x%2B35
y%3E=-%283%2F5%29x%2B7
graph%28300%2C300%2C-2%2C10%2C-2%2C10%2Cy%3E=-%283%2F5%29x%2B7%29
.
.
2x%2By%3C=14
y%3C=-2x%2B14
.
.
graph%28300%2C300%2C-2%2C10%2C-2%2C10%2Cy%3C=-2x%2B14%29
.
.

The easy vertices are (0,0),(0,7),(7,0).
To find the remaining one, set the two linear equations equal to each other.
-2x%2B14=-%283%2F5%29x%2B7
-2x%2B%283%2F5%29x=-7
-%2810%2F5%29x%2B%283%2F5%29x=-7
-%287%2F5%29x=-7
x=5
Then,
y=-2%285%29%2B14
y=4
(5,4) is the final vertex.
Now check the function at each point.
.
.
.
(0,0):P=3%280%29%2B2%280%29=0<-- Min
(7,0):P=3%287%29%2B2%280%29=21
(0,7):P=3%280%29%2B2%287%29=14
(5,4):P=3%285%29%2B2%284%29=23<-- Max