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Gnom [1K]
1 year ago
10

See attachment for the full question

Mathematics
1 answer:
alexandr402 [8]1 year ago
3 0

The inverse of the demand function is; P = 9 - 0.25Q

The profit-maximizing price and quantity are; $8.5 and 2 units.

The maximum profit is; $1

<h3>How to find the inverse of a function?</h3>

A) The demand function we are given is;

Q = 36 - 4P

Making P the subject gives the inverse demand function;

P = (36 - Q)/4

P = 9 - Q/4

P = 9 - 0.25Q

B) The profit-maximization point is the point at which MR = MC.

MR refers to the marginal revenue and MC is the marginal cost.

MC can be calculated as the first derivative of the cost function:

C(Q) = 4 + 4Q + Q²

MC = C'(Q) = 2Q + 4

Total Revenue = Price * Quantity

Total Revenue = (9 - 0.25Q) * Q

Total Revenue = 9Q - 0.25Q²

MR is gotten by differentiating Total Revenue to get;

MR = 9 - 0.5Q

Applying the condition MR = MC, we have;

9 - 0.5Q = 4 - 2Q

Solving for Q gives Q = 2

Thus, profit maximizing quantity is 2.

Thus, profit maximizing price will be;

P(2) = 9 - 0.25(2)

P(2) = $8.5

C) Formula for Maximum Profit is;

Profit = Total Revenue - Total Cost

Total Revenue = 8.5 * 2

Total revenue = $17

Total Cost is;

C(2) = 4 + 4(2) + 2²

C(2) = $16

Thus;

Maximum Profit = 17 - 16 = $1

Read more about Inverse of a function at; brainly.com/question/13948067

#SPJ1

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Answer:

(\frac{f}{g})(x)=\frac{f(x)}{g(x)}\\\\(\frac{f}{g})(7)=\frac{f(7)}{g(7)}

Step-by-step explanation:

Division operation of function:If\ f(x)\ and\ g(x)\ are\ two\ functions\ then\ (\frac{f}{g})(x)=\frac{f(x)}{g(x)}

Here\ we\ have\ to\ find\ (\frac{f}{g})(7)\\\\(\frac{f}{g})(7)=\frac{f(7)}{g(7)}

Example:

Take\ f(x)=3x^2+1,\ g(x)=x+1\\\\(\frac{f}{g})(x)=\frac{f(x)}{g(x)}\\\\(\frac{f}{g})(x)=\frac{3x^2+1}{x+1}\\\\f(7)=3\times 7^2+1\\\\f(7)=3\times 49+1\\\\f(7)=148\\\\g(7)=7+1\\\\g(7)=8\\\\(\frac{f}{g})(7)=\frac{f(7)}{g(7)}\\\\(\frac{f}{g})(x)=\frac{148}{8}

7 0
3 years ago
Someone help me please !
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PLEASE help !!! I’m struggling and I suck at math. Can someone answer this for me? For points and brainly !
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Answer:

\huge\boxed{2329 \ \text{pounds}}

Step-by-step explanation:

In order to solve this equation, let's see what we already know.

  • We know two points on the graph <em>which we can use to find the slope</em>

That's about it.

However, this can come useful to find the slope between the two points, which is the slope for the entire graph (since this is linear). The slope between two points is usually defined as \frac{\Delta y}{\Delta x} (change in y / change in x). Our two points are (18, 2017) and (48, 2212).

The change in y between our two points is 2212-2017 = 195, and the change in x is 48 - 18 = 30. Our slope will then be \frac{195}{30}, which comes out to be approximately 6.5. Therefore, our slope is 6.5.

Now that we know the slope, we can substitute inside our equation in slope intercept form.

y = 6.5x+b

We have yet to find b, the y-intercept (how much the plane itself weighs). To find b, we can substitute a point on the graph into the equation and solve for b. We know that the point (18, 2017) is on the graph so let's use that.

  • 2017 = 6.5 \cdot18 + b
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Now that we know our y-intercept is 1900, we can create our equation by using the slope and the y-intercept.

y=6.5x+1900

Finally, to find the weight of the plane with 66 pounds of fuel, we can substitute 66 inside this equation as x.

  • y = 6.5 \cdot66+ 1900
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  • y=2329

So the plane weighed 2329 pounds with 66 gallons of fuel.

Hope this helped!

7 0
2 years ago
Read 2 more answers
Gretchen can buy 17.4 ounces of Brand A toothpaste for $5.22, or she can buy 26.6 ounces of Brand B toothpaste for $6.65. Which
konstantin123 [22]
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Price of Brand B toothpaste for 1 ounces = $6.65/26.6 = 0.25
So, if we see the price for per ounce of brand A and B, price of Brand B per ounce is less than brand A.
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Thus, the correct answer is "D", <span>Brand B is the better deal, because it costs $0.05 less per ounce than Brand A".</span>
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