Question

. Let x and y be two positive numbers such the sum is 175 and (x+3) (y+4) is a maximum.

Answer 1

since \(x+y=175\) you have \(y=175-x\)
maximize \((x+3)(175-x+4)\) after doing some algebra first

Answer 2

Oh so you don't start with the (x+3) and (y+4)= 175?

Answer 3

So you first find x then input X to maximize?

Answer 4

it says "the sum is 175" which translates as \(x+y=175\)

Answer 5

yeah find the value of \(x\) that gives the max
it is a quadratic, so the max is at the vertex

Answer 6

you good from there?

Answer 7

Yeah so I found X= 175/2. In order to find Y. I must input x to the equation. (175/2 + 3) (y + 4) = 175?

Answer 8

some mistake there i think

Answer 9

\[(x+3)(175-x+4)=(x+3)(179-x)=-x^2+176 x+537\]

Answer 10

then vertex is at \(\frac{176}{2}=88\)

Answer 11

Does this relate to Optimization because I taught I was supposed to find a x and y coordinate?

Answer 12

you have \(x=88\) and since \(x+y=175\) you can certainly find \(y\) and also you can find \((x+3)(y+4)\)

Answer 13

Oh alright now I get it thanks.

Answer 14

yw