Finding minimum and maximum values of f (x, y)

[samistumbo]

I know you all REALLY hate it when someone posts on here and doesn't show you what we already know. BUT I don't know where to begin on this on.
&I need it dumbed... like every part explained.... because this one got me and my tutor wanted to skip it. lol

Find the minimum and maximum values of f (x,y) if f(x,y)= 3x + 4y, and the domain S of f is defined by the simultaneous inequalities x + y ≥ 2, y ≤ 3x + 2, 5x ≤ 10 - y.

 

[tkhunny]

BUT I don't know where to begin on this on.

You absolutely MUST give this up. Let go of your need to know where to begin. Much of the teaching of mathematics is to train the student how to think. It's in your brain. Let it out!

Can you graph the three inequalities on a single set of coordinate axes?

Can you define the extent of the triangular region in the first quadrant?

What is the nature of your f(x,y)? Does it have cusps, or saddles, or bowls, or caps, or twists, or waves? Does the gradient exist everywhere in the Domain? How tricky is the gradient?

Really, as long as you have a brain, there is no excuse for "no idea". Please think more of yourself than that.

 

[burakaltr]

I know you all REALLY hate it when someone posts on here and doesn't show you what we already know. BUT I don't know where to begin on this on.
&I need it dumbed... like every part explained.... because this one got me and my tutor wanted to skip it. lol

Find the minimum and maximum values of f (x,y) if f(x,y)= 3x + 4y, and the domain S of f is defined by the simultaneous inequalities x + y ≥ 2, y ≤ 3x + 2, 5x ≤ 10 - y.

Set del(f(x,y))/ delx = 0 and simultaneously

del(f(x,y))/ dely = 0

and solve for maxima and minima

 

[samistumbo]

You absolutely MUST give this up. Let go of your need to know where to begin. Much of the teaching of mathematics is to train the student how to think. It's in your brain. Let it out!

Can you graph the three inequalities on a single set of coordinate axes?

Can you define the extent of the triangular region in the first quadrant?

What is the nature of your f(x,y)? Does it have cusps, or saddles, or bowls, or caps, or twists, or waves? Does the gradient exist everywhere in the Domain? How tricky is the gradient?

Really, as long as you have a brain, there is no excuse for "no idea". Please think more of yourself than that.

I was able to graph it and came up with three points, (0,2), (2,0), and (1,5).

But then I am not sure if I did it right from there on..... and I apologize but most often when I state that I don't know where to start, I really don't know where to start. I have always struggled in math... and I am trying my hardest in this calculus class and reading everything but it's online and it's hard to teach myself calculus when I've not seen any math in 6 years. Usually though, if someone can show me how to do something once, then I can do it again and again. Just hard to always find examples for everything, so I come here.

 

[tkhunny]

You should not get threee points. Those are not equalities. They are inequalities.

Interestingly, you may need only the points of intersection (vertices of the triangula region). Give this some thought.

Substitute "M" = f(x,y) and solve the equation for y. See if anything makes a little more sense.