from the linear example so far I have...
Profit = 20X + 16Y
and the constraints are:
X + 2Y ≤ 480
3X + 4Y≤1080
How do I show the Feasible Region and the Optimal Point on a graph.??
Hello bobchiba,
I'm assuming that $\displaystyle x \ge 0$ and $\displaystyle y \ge 0$.
Graph the two equalities:
$\displaystyle x+2y=480$ and $\displaystyle 3x+4y=1080$
Shade the appropriate regions indicated by the inequalities and find where they overlap. This is your feasible region.
Three of the vertices lie on the axes: (0, 0), (360, 0) , and (0, 240).
To find the 4th vertex, solve the two linear equations for their intersection point.
See attachment.
Then to find your optimal point or wher the profit function produces the largest value, substitute each vertex coordinates into your function and see what comes out.
Okay; then follow the exact same graphing, corner-finding, and evaluating process outlined, but using your inequalities instead of the standard ones guessed in that earlier reply.
If you get stuck, please reply showing (or describing) your work and reasoning, clearly stating where you are having difficulty. Thank you!