SOLUTION: Hello, I need help!! The following model represents an optimization problem. Determine the maximum solution by graphing the boundary lines, shading the appropriate region and l

Question 1087591: Hello, I need help!!
The following model represents an optimization problem. Determine the maximum solution by graphing the boundary lines, shading the appropriate region and looking for points of intersection in the feasible solution.
so I need to point this on the graph.. help thanks!!
Restrictions:
XEW
YEW
Contraints:
x > 0
y > 0
5x (greater or equal to) y + 5
x + y (less than or equal to) 25
Onjective function:
A = x + 2y

Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
using www.desmos.com/calculator, this becomes relatively easy.

you constraints are:

x >= 0
y >= 0
5x >= y + 5
x + y <= 25

note that x >= 0 and not x > 0 because x can't be negative and 0 is not negative.

same for y >= 0 rather than y > 0.

your objective function is:

A = x + 2y

you want to maximize A.

using the desmoc.com calculator, you would graph the opposite of the inequality constraints.

therefore, you would graph:

x <= 0
y <= 0
5x <= y + 5
x + y >= 25

your graph will look like this:

$$$

your feasible region is the area of the graph that is NOT shaded.

the corner points of your feasible region are:

(5,20)
(1,0)
(25,0)

your objective function is x + 2y.

since you want to maximize your objective function, you will look for the corner points that has the greatest value.

the value of your object function at each of these corner points respectively is:

(5,20) = 45
(1,0) = 1
(25,0) = 25

your maximum solution is 45 at (5,20)

all your constraints are met when x = 5 and y = 20.

x >= 0 becomes 5 >= 0 which is good.
y >= 0 becomes 20 >= 0 which is good.
5x <= y + 5 becomes 25 <= 25 which is good.
x + y >= 25 becomes 25 >= 25 which is good.

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