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3 years ago

A) - 17 B B)7 4. 3591 C) | D 12

Mathematics

1 answer:

vladimir1956 [14]3 years ago

8 0

Answer:

Step-by-step explanation:

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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

3 years ago

PLS HELP WILL MARK BRAINLIEST

ahrayia [7]

9(2j+7+5j) Foil this out to get 18j+7+45j then 63j+7

Answer: 18j+7+45j , 63j+7 I think

8 0

3 years ago

Read 2 more answers

I need help with these two

Alika [10]

Answer:

19. A

20. A

Step-by-step explanation:

19. tan(53)=15/x

x(tan(53))=15

x=15/(tan53))

x=11.3 feet

20. tan(60)=12/x

x(tan(60))=12

x=12/(tan(60))

x=6.93, or 4sqrt3

4 0

3 years ago

Graph a system of equations to solve log (−5.6x + 1.3) = −1 − x. Round to the nearest tenth.

Neporo4naja [7]

Answer:

Step-by-step explanation:

-2.1 and 0.2

8 0

3 years ago

A survey of the whole United States shows that 75% of 6th grade students like sports that involve running, that 60% of boys like

slamgirl [31]

Answer: 75% of 6th Grade Students

Step-by-step explanation:

This sample makes the most sense because it is a majority of everyone, not just a majority of certain people. Also, Mountain School would get fewer complaints from other people if they went with a majority of 75%. Finally, running sports usually cost less then other sports.

3 0

2 years ago