<p>Hey everyone, I have a quick math question here that I couldn't find a suitable thread for (sorry if that upsets anyone).</p>
<p>This is from the April ACT. They give you three requirements: </p>
<ol>
<li>y > or = 0</li>
<li>y < or = 2x + 4</li>
<li>y < or = -x + 4</li>
</ol>
<p>P(x,y) = 4x + 3y</p>
<p>They ask what the maximum value of P(x,y) when x and y satisfy the 3 conditions given.</p>
<p>A. 4
B. 8
C. 12
D. 16
E. 28</p>
<p>I'm at a loss for how to solve this, so any help would be appreciated!</p>
<p>Is it A? I’ll explain how I arrived at it if you give the right answer! :)</p>
<p>can someone answer this with an explanation?</p>
<p>My answer is D, 16. I got this answer by graphing the three inequalities which gives you a triangular shaped union with vertices at (-2,0), (0,4), and (4,0). From here you can use common sense and process of elimination (assuming you don’t know calculus) to determine the maximum value of 4x + 3y. Note first that the maximum value will not be found by any points in the second quadrant. Now we can focus on the area in the first quadrant. It should be relatively clear that our maximum value will be found along the edges (and as you will soon see, on a vertex). So we set up a system of equations: x + y = 4 and 4x + y = ? Solving in terms of x (you could also do y) we get x + 12 = ? However, our restriction is that x < or equal to 4. Obviously, our maximum value will be when x is maximized hence the maximum value P(x,y) is at (4,0) and is 4(4) + 3(0) = 16.</p>
<p>grey wolf, you are correct. They actually GIVE you the triangle that you graphed, so you didn’t even have to do that. you just need to plug in the points (0,4) and (4,0) and see which gives you the maximum value. So, 16 is correct. ( using (4,0).</p>
<p>Well this is wonderful, thanks a lot!</p>
<p>There was one today like that, where they asked for the maximum value. I believe the answer was 22 and was found through substituting the x and y values into its respective equation.</p>
<p>Thanks again!</p>