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vaieri [72.5K]
3 years ago
12

What is the maximum value of P = 4x + 2y, given the constraints on x and y listed below?

Mathematics
2 answers:
leva [86]3 years ago
8 0

Answer:

P < 28

Step-by-step explanation:

given the constraints:

x + 2y < 10

y < 2

x>0

y>0

we can see that the range of y is from 0 to 2: 0

we can use the maximum value of y in x+2y<10, to find the range of x

x + 2y < 10

x + 2(2) < 10

x < 10 -4

x < 6

now we know that range of x is from 0 to 6: 0

take a closer look at these ranges, both of the ranges of x and y don't include their extreme values. (these are not 0\leq x\leq 6,\,\,0\leq y\leq 2 )

The function P is:

P = 4x + 2y, we can easily put in all the maximum ranges of x and y in the equation to find the maximum value of P. but before plugging in the values we must be careful: we are putting the extremes of the ranges in the equation, but these extremes are not in the actual range itself.

so instead of writing that the maximum value of P is equal to a number, we should write that the maximum value of P is close to that number(or approaching that number from below)

P < 4(6) + 2(2)

P < 28

NOTE:

if the constraints given include the extremes of the ranges. Then the answer will be P = 28.

Aliun [14]3 years ago
6 0
What are the constraints?


When you graph the constraints the four points you can use are (0,0), (10,0), (0,2), and (6,2). 

(10,0) is the point that gives you the maximum value which is 40.
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The average annual income I in dollars of a lawyer with an age of x years is modeled with the following function I=425x^2+45,500
natali 33 [55]
You did not include the questions, but I will give you two questions related with this same statement, and so you will learn how to work with it.

Also, you made a little (but important) typo.

The right equation for the annual income is: I = - 425x^2 + 45500 - 650000

1) Determine <span>the youngest age for which the average income of a lawyer is $450,000

=> I = 450,000 = - 425x^2 + 45,500x - 650,000

=> 425x^2 - 45,000x + 650,000 + 450,000 = 0

=> 425x^2 - 45,000x + 1,100,000 = 0

You can use the quatratic equation to solve that equation:

x = [ 45,000 +/- √ { (45,000)^2 - 4(425)(1,100,000)} ] / (2*425)

x = 38.29 and x = 67.59

So, the youngest age is 38.29 years

2) Other question is what is the maximum average annual income a layer</span> can earn.

That means you have to find the maximum for the function - 425x^2 + 45500x - 650000

As you are in college you can use derivatives to find maxima or minima.

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=> x = 45500 / 900 = 50.55

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3 years ago
What’s the correct representation of six over one?
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Answer:

6

Step-by-step explanation:

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Point D is in the interior of ZABC, m ABC = 10x - 7, m_ABD = 6x + 5, and m DBC = 36. What is m ABD?
mestny [16]

Answer:

<h3>77</h3>

Step-by-step explanation:

If Point D is in the interior of <ABC, then <ABD+<BDC = <ABC

Given

<ABC = 10x - 7,

<ABD = 6x + 5

<DBC = 36

Substituting the given parameters into the formula above;

ABD+<DBC = <ABC

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collect like terms

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divide both sides by -4

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