Which graphed matches the equation ?

A bakery finds that the price they can sell cakes is given by the function p = 580 − 10x where x is the number of cakes sold per

dexar [7]

Answer:

The total revenue is $TR=580x-10x^2$ .

The marginal revenue is $MR=580-20x$ .

The fixed cost is $900.

The marginal cost function is $MC=50x+300$ .

Step-by-step explanation:

The Total Revenue ( $TR$ ) received from the sale of $x$ goods at price $p$ is given by

$TR=p\cdot x$

The Marginal Revenue ( $MR$ ) is the derivative of total revenue with respect to demand and is given by

$MR=\frac{d(TR)}{dx}$

From the information given we know that the price they can sell cakes is given by the function $p=580-10x$ , where $x$ is the number of cakes sold per day.

So, the total revenue is

$TR=(580-10x)\cdot x\\TR=580x-10x^2$

And the marginal revenue is

$MR=\frac{d}{dx}(580x-10x^2) \\\\\mathrm{Apply\:the\:Sum/Difference\:Rule}:\quad \left(f\pm g\right)'=f\:'\pm g'\\\\MR=\frac{d}{dx}\left(580x\right)-\frac{d}{dx}\left(10x^2\right)\\\\MR=580-20x$

The Fixed Cost ( $FC$ ) is the amount of money you have to spend regardless of how many items you produce.

The Marginal Cost ( $MC$ ) function is the derivative of the cost function and is given by

$MC=\frac{d(TC)}{dx}$

We know that the total cost function of the company is given by $C=(30+5x)^2$ , which it is equal to

$\mathrm{Apply\:Perfect\:Square\:Formula}:\quad \left(a+b\right)^2=a^2+2ab+b^2\\a=30,\:\:b=5x\\\\\left(30+5x\right)^2=30^2+2\cdot \:30\cdot \:5x+\left(5x\right)^2=25x^2+300x+900\\\\C=25x^2+300x+900$

From the total cost function and applying the definition of fixed cost, the fixed cost is $900.

And the marginal cost function is

$MC=\frac{d}{\:dx}\left(25x^2+300x+900\right)\\\\MC=\frac{d}{dx}\left(25x^2\right)+\frac{d}{dx}\left(300x\right)+\frac{d}{dx}\left(900\right)\\\\MC=50x+300+0=50x+300$

4 0

3 years ago

Two people are swinging a jump rope. The height of the middle of the rope, in inches, can be modeled by a cosine function with a

Tju [1.3M]

Answer:

B. 75 inches

Step-by-step explanation:

just took the test

3 0

3 years ago

Read 2 more answers

2. The direct distance between city A and city B is 200 miles. The direct distance

Misha Larkins [42]

Answer:

2

Step-by-step explanation:

8 0

3 years ago

What is a solution I forgot the inequality M > 13/6

o-na [289]

The solution can be anything bigger than 13/6.

For example: 3, 4, 5, 6...ect

7 0

3 years ago

Suppose a set of data about the spread (in hundreds of acres) of a food-borne bacteria (after t weeks) in lettuce has the follow

Alexxandr [17]

Answer:

A sinusoidal model would be used

The kind of function that have consistency in the periodic rate of change is the Average rate of changes

Step-by-step explanation:

The type of model that would be used is sinusoidal model and this is because there is periodic change in the values given ( i.e the rate of changes given )

For percentage rate of changes :

starting from 0.9% there is an increase to 1.3% then a decrease to 1.1% and a further decrease to 1% before an increase to 1.3% and another decrease to 1%

For Average rate of changes:

starting from 2.9 there is a decrease to 2.4, then an increase to 3.7 and another decrease to 3.1 followed by an increase to 3.6 and a decrease back to 3.2

This relation ( sinusoidal model ) is best suited for a linear model because there is a periodic rate of change in the functions

The kind of function that have consistency in the period rate of change is the Average rate of changes

6 0

3 years ago