Question

Algebra II question.
So today my teacher is giving us something new to cover an I can't seem to get my grasp around it so can anyone help me?
The worksheet asks us to solve the system of constraint and find the value of x and y that maximize the objective function. How would I go about solve a question like this? I tried graphing but I do not know where to go from there.

Answer 1

this is linear programming...this may help explain it for you
http://www.purplemath.com/modules/linprog.htm

Answer 2

\[Constraints \left[ x \ge 0, ~y \ge 0, ~y \le \frac{1}{2}x + 2,~ 5\ge y + x \right]\]
\[5\ge y + x \Rightarrow y \le 5 -x\]
My objective function is \(c = 7x - 3y\).

Is that anything like I'm supposed to do?

Answer 3

yes now shade in region defined by inequalities
plug in points at corners of shaded region

Answer 4

(0, 2), (5, 0), (0, 0)
Do I plug in those points into the objective function?
\[c=7x−3y \Rightarrow c = 7(0)-3(2) \Rightarrow c = -6\]
\[c=7x−3y \Rightarrow c = 7(5)-3(0) \Rightarrow c = 35\]
\[c=7x−3y \Rightarrow c = 7(0)-3(0) \Rightarrow c = 0\]

Answer 5

yes, but also the point where the lines cross
5-x = 1/5x + 2

Answer 6

of course since 7x-3y will only get smaller when y gets larger....th max occurs at point (5,0)

Answer 7

I think I get it :) Thank you so much sir!

Answer 8

yw :)