Answer:
We know that the map is of North America:
The probabilities are:
1) North America:
As the map is a map of North America, you can point at any part of the map and you will be pointing at North America, so the probability is p = 1
or 100% in percentage form.
2) New York City.
Here we can think this as:
The map of North America is an extension of area, and New Yorck City has a given area.
As larger is the area of the city, more probable to being randomly choosen, so to find the exact probability we need to find the quotient between the area of New York City and the total area of North America:
New York City = 730km^2
North America = 24,709,000 km^2
So the probability of randomly pointing at New York City is:
P = ( 730km^2)/(24,709,000 km^2) = 3x10^-5 or 0.003%
3) Europe:
As this is a map of Noth America, you can not randomly point at Europe in it (Europe is other continent).
So the probaility is 0 or 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
This state action is referred to as monadic. This is a function or a relation with an arity of one. A monad can relate an algebraic theory into a <span>composition of a function though its power is not always apparent.</span>
