Linear equation solvle.?

Question

A cafe can only produce a total of 500 teas and cakes daily, and can only make less than 150 cakes and 450 teas each day. The profit earned on tea is 50 cent and the profit from the sale of a cake is 80 cent. How many teas and cakes should be brewed and baked to maximize the cafe's profit?

x= teas per day
y= cakes per day
p= 0.5x + 0.8y
*<= means less than and equal to
0 <= x <= 450
0 <= y <= 150
x +y <= 500
Is this right? And if so..

1)Can someone draw the graph and show me a link,
2)List the coordinate of extreme points,
3)How many of teas and cakes will bring the greatest profit?

Thank you!!

I just want to know the extreme points,
that is enough.
And if this problem make sense?

Answer 1

You set it up correctly!

Now, here's how to draw your own graph. You have five different <= inequalities. Turn then all into equations by substituting in =. Each gives a line. Draw the five lines (four of which are on or parallel to one of the two axes). They bound an irregular pentagon. That pentagon is the feasible set.

Since the objective function is linear, it will surely be maximized at one or more of the vertices.