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Artist 52 [7]
2 years ago
12

Suppose total benefits and total costs are given by b(y) = 100y − 8y2 and c(y) = 10y2. what is the maximum level of net benefits

(rounded to the nearest whole number)?
Mathematics
1 answer:
olga nikolaevna [1]2 years ago
3 0
Whenever you face the problem that deals with maxima or minima you should keep in mind that minima/maxima of a function is always a point where it's derivative is equal to zero.
To solve your problem we first need to find an equation of net benefits. Net benefits are expressed as a difference between total benefits and total cost. We can denote this function with B(y).

B(y)=b-c
B(y)=100y-18y²

Now that we have a net benefits function we need find it's derivate with respect to y.

\frac{dB(y)}{dy} =100-36y

Now we must find at which point this function is equal to zero.

0=100-36y
36y=100
y=2.8

Now that we know at which point our function reaches maxima we just plug that number back into our equation for net benefits and we get our answer.

B(2.8)=100(2.8)-18(2.8)²=138.88≈139.

One thing that always helps is to have your function graphed. It will give you a good insight into how your function behaves and allow you to identify minima/maxima points.


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Hope this helps you.

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Brad goes to the deli. He sees that chicken costs $2.50 per pound. He wants to buy 1/2 pound of chicken. He pays with a $10 bill
andreyandreev [35.5K]

Answer:

8.75

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Gabrielle's age is three times Mikhail's age. The sum of their ages is 20. What is Mikhail's age?
PtichkaEL [24]

Answer:

Mikhail is 5 years old

Step-by-step explanation:

Represent each member with a variable.

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X=3y (Gabrille is 3 times Mikhails age)

Substitute 3Y into the first equation (simultaneous equation)

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To check your answer.

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Answer:

  1/3

Step-by-step explanation:

The slope of a line is the ratio of its "rise" to its "run." The "rise" is the change in vertical distance, and the "run" is the corresponding change in horizontal distance between two points on the line. The formula for the slope is ...

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_____

<em>Additional comment</em>

A line through the origin is the graph of a <em>proportional</em> relationship. That is, y is proportional to x. The slope of the line is the <em>constant of proportionality</em>. The equation of the line is ...

  y = kx . . . . . . where k is the constant of proportionality.

The line in this problem statement will have the equation ...

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