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
Answer: 3000 gallon
Step-by-step explanation:
Here, The total quantity of 15% alcohol content = 3000 gallon
And, in which quantity of alcohol = 15% of 3000 gallon = 450 gallon.
Let the total quantity of 9% alcohol content = x
In which quantity of alcohol = 9% of x gallon= 9x/100 gallon
Now, according to the question, The wine with a 9% alcohol content will be mixed with 3,000 gallons of wine with a 15% alcohol content in order to achieve the desired 12% alcohol content.
Thus, the total quantity of mixture of 12% alcohol content = The total quantity of 15% alcohol content + total quantity of 9% alcohol content
= 3000 + x
In which quantity of alcohol = 12 % of ( 3000+x) = (360 + 12x/100) gallon ---(1)
But, the quantity of alcohol in 12 % of alcohol content = quantity of alcohol in 15% of alcohol content + quantity of alcohol in 9% of alcohol content
The quantity of alcohol in 12 % of alcohol content = (450 + 9x/100) gallon ---(2)
On equating equation (1) and (2)
We get, 360 + 12x/100 = 450 + 9x/100
⇒ 3x/100 = 90
⇒ x = 3000
Therefore, The total quantity of the mixture of 9% alcohol content = 3000
Answer:
The answer is
<h2>9 units</h2>
Step-by-step explanation:
The distance between two points can be found by using the formula
<h3>
</h3>
where
(x1 , y1) and (x2 , y2) are the points
From the question the points are
(6,-5) and (-3,-5)
The distance between them is
<h3>
</h3>
We have the final answer as
<h3>9 units</h3>
Hope this helps you
Area= base + base / 2 then multiply the height.
Example: 6+7 /2*6= 39
You know that there are 25 people and each person had 36 carrots. To find how many carrots everyone has in total, you have to multiply 25 by 36.
25 times 36 is 900.
There are 900 carrots altogether.
