Someone help me this is due tm

QUESTION 3 [10 MARKS] A bakery finds that the price they can sell cakes is given by the function p = 580 − 10x where x is the nu

Harman [31]

Answer:

(a)Revenue function, $R(x)=580x-x^2$

Marginal Revenue function, R'(x)=580-2x

(b)Fixed cost =900 .

Marginal Cost Function=300+50x

(c)Profit, $P(x)=-35x^2+280x-900$

(d)x=4

Step-by-step explanation:

Part A

Price Function $= 580 - 10x$

The revenue function

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

The marginal revenue function

$\dfrac{dR}{dx}= \dfrac{d}{dx}(R(x))=\dfrac{d}{dx}(580x-x^2)=580-2x\\R'(x)=580-2x$

Part B

(Fixed Cost)

The total cost function of the company is given by $c=(30+5x)^2$

We expand the expression

$(30+5x)^2=(30+5x)(30+5x)=900+300x+25x^2$

Therefore, the fixed cost is 900 .

Marginal Cost Function

If $c=900+300x+25x^2$

Marginal Cost Function, $\frac{dc}{dx}= (900+300x+25x^2)'=300+50x$

Part C

Profit Function

Profit=Revenue -Total cost

$580x-10x^2-(900+300x+25x^2)\\580x-10x^2-900-300x-25x^2\\$Profit,P(x)=-35x^2+280x-900$

Part D

To maximize profit, we find the derivative of the profit function, equate it to zero and solve for x.

$P(x)=-35x^2+280x-900\\P'(x)=-70x+280\\-70x+280=0\\-70x=-280\\$Divide both sides by -70\\x=4$

The number of cakes that maximizes profit is 4.

6 0

2 years ago

jacob wants to buy packets of fruit juice. on tuesday, he buys 8 packets of orange and 6 packets of Apple the packets make a tot

ioda

Answer:

Each packet of orange can make 2 cups of juice and each packets of Apple can make 3 cups of juice.

Step-by-step explanation:

Let number of cups of juice in each packet of orange be 'x'.

Let number of cups of juice in each pack of apples be 'y'.

Given:

On Tuesday;

Number of packets of oranges = 8

Number of packets of apples = 6 packets.

Amount of fruit juice = 34 cups

So we can say that;

Amount of fruit juice is equal to sum of Number of packets of oranges multiplied by number of cups of juice in each packet of orange and Number of packets of apples multiplied by number of cups of juice in each pack of apples.

framing in equation form we get;

$8x+6y=34 \ \ \ \ equation \ 1$

On Wednesday;

Number of packets of oranges = 14

Number of packets of apples = 6

Amount of fruit juice = 46 cups

So we can say that;

Amount of fruit juice is equal to sum of Number of packets of oranges multiplied by number of cups of juice in each packet of orange and Number of packets of apples multiplied by number of cups of juice in each pack of apples.

framing in equation form we get;

$14x+6y=46 \ \ \ \ equation \ 2$

Now Subtracting equation 1 from equation we get;

$14x+6y-(8x+6y)=46-34\\\\14x+6y-8x-6y=12\\\\6x=12$

Now dividing both side by 6 we get;

$\frac{6x}{6}=\frac{12}{6}\\\\x=2\ cups$

Now we will substitute the value of 'x' in equation 1 we get;

$8x+6y=34\\\\8\times2+6y=34\\\\16+6y=34$

Subtracting both side by 16 we get;

$16+6y-16=34-16\\\\6y= 18$

Now dividing both side by 6 we get;

$\frac{6y}{6}=\frac{18}{6}\\\\y=3$

Hence Each packet of orange can make 2 cups of juice and each packets of Apple can make 3 cups of juice.

5 0

2 years ago

PLS HELP HELP PLSZZZZZ

Dmitry_Shevchenko [17]

Answer:

cant see the pic.

Step-by-step explanation:

4 0

2 years ago

Read 2 more answers

Me dicen la sifra 5p-14=8p+19

Alex

5p-14=8p+19
8p-5p = -3p
-3p-14=18
14+18 = 33
33/-3=-11

7 0

2 years ago

The first quartile of the dataset {1, 2, 3, 4, 5, 6} is _______. (give your answer as a whole number.

notsponge [240]

The first quartile of the dataset {1, 2, 3, 4, 5, 6} is 2.

Given data set: {1,2,3,4,5,6}

Median of the given data set =3.5

The data set can be split into 2 parts as, {1,2,3} and {4,5,6}. The first quartile is calculated by simply finding the median of the first part of the data set.

Thus, the first quartile is 2.

The quarter divides the distribution into four groups and calculates the range of values above and below the mean.

A quartile separates the dataset into four categories by dividing the data into three points: the lowest, median, and upper quartiles.

The interquartile range, a measurement of variation around the median, is calculated using quartiles.

Learn more about quartiles here:

brainly.com/question/10005803

#SPJ4

5 0

1 year ago