I have corner points of:

Mathematics

1 answer:

WARRIOR [948]3 years ago

7 0

The points you found are the vertices of the feasible region. I agree with the first three points you got. However, the last point should be (25/11, 35/11). This point is at the of the intersection of the two lines 8x-y = 15 and 3x+y = 10

So the four vertex points are:
(1,9)
(1,7)
(3,9)
(25/11, 35/11)

Plug each of those points, one at a time, into the objective function z = 7x+2y. The goal is to find the largest value of z

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Plug in (x,y) = (1,9)
z = 7x+2y
z = 7(1)+2(9)
z = 7+18
z = 25
We'll use this value later.
So let's call it A. Let A = 25

Plug in (x,y) = (1,7)
z = 7x+2y
z = 7(1)+2(7)
z = 7+14
z = 21
Call this value B = 21 so we can refer to it later

Plug in (x,y) = (3,9)
z = 7x+2y
z = 7(3)+2(9)
z = 21+18
z = 39
Let C = 39 so we can use it later

Finally, plug in (x,y) = (25/11, 35/11)
z = 7x+2y
z = 7(25/11)+2(35/11)
z = 175/11 + 70/11
z = 245/11
z = 22.2727 which is approximate
Let D = 22.2727

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In summary, we found
A = 25
B = 21
C = 39
D = 22.2727

The value C = 39 is the largest of the four results. This value corresponded to (x,y) = (3,9)

Therefore the max value of z is z = 39 and it happens when (x,y) = (3,9)

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Final Answer: 39

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Solve for x.<br> Sqrt8 (Sqrt2 - x) = 11

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Answer: $\frac{-7\sqrt{2} }{4}$

Step-by-step explanation:

So first, let's get rid of the parentheses. We can multiply it out to get $\sqrt{16}-x\sqrt{8} =11$ . We know that the square root of 16 is ±4, so now our equation is ±4 - $x\sqrt{8}$ =11. I'm guessing since the problem only has one solution it's most likely only positive 4, so let's revise our equation to 4 - $x\sqrt{8}$ =11. We can use inverse operations to make the a little easier to solve: -7= $x\sqrt{8}$ . We divide both sides by $\sqrt{8}$ to get $\frac{-7}{\sqrt{8} } =x$ , which we can rationalize (remove the square root from the denominator so that it's a proper answer) by multiplying by $\frac{\sqrt{8} }{\sqrt{8} }$ (which is equal to one so we can use it) which is equal to $\frac{-7\sqrt{8} }{8}$ . Let's finish this by simplifying it. $\sqrt{8} =2\sqrt{2}$ (2x $2^{2}$ ). We can simplify it further by simplifying the 2, making it $\frac{-7\sqrt{2} }{4}$ .