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3 years ago

!!!HELP PLEASE !!!!!

Mathematics

1 answer:

Fofino [41]3 years ago

8 0

Tree 3 diagram is the answer

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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

Alicia bought a frozen lemonade for $3.71. She gave the clerk a $5 bill. How much change should she receive?

Grace [21]

5 - 3.71 = $1.29
hope this helps! :)

8 0

2 years ago

Read 2 more answers

I need to know how to round to the nearest hundredth in the number 1.120

ryzh [129]

You can either round to 1000 or 2000 but 1.120 is closer to 1000

8 0

3 years ago

Read 2 more answers

Choose the polynomial that is written in standard form 7x^5+8x^8+27x

Nataliya [291]

Answer: Option d: -3*x^4*y + 2*x^2*y^2 + 5*y^3

Step-by-step explanation:

In standard form, the first term of the polynomial must be the term with the highest degree and on each subsequent term the degree decreases. In the case of two variables, the degree is equal to the sum of the exponents.

Then the correct option is d.

Where the degree of the first term is (4 + 1) = 5

The degree of the second term is (2 + 2) = 4

The degree of the third therm is 3.

We can see that the degree decreases as the term number increases, then the polynomial written in standard form is:

-3*x^4*y + 2*x^2*y^2 + 5*y^3

8 0

2 years ago

Select the proper order from the least to the greatest 1/2 5/6 2/7 4/2

Olin [163]

Answer:

1/2, 2/7, 5/6, 4/2

Step-by-step explanation:

4 0

2 years ago