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VladimirAG [237]
3 years ago
9

50 points!

Mathematics
1 answer:
jekas [21]3 years ago
3 0

Answer:

Attaching answer for 1 below!!

2. C. -- y=2x+9

3. B. -- y=5/3x+3

Step-by-step explanation:

1.  First screenshot below

2. To convert standard equations (Ax+By=C)  to slope intercept (y=mx+b), what you do is preform inverse operations on A to both sides (modeled below).  Then, the equation will look like this; By= -Ax+C.  The last thing you need to do to cancel out B from the y is divide both sides by B, and you'll have your answer.  So, I did that exact process with the equation and that's how I got C.  Now, when you have no number next to the y, you don't need to divide, so it's a very simple process that way.

-2x+y=9

+2          +2

3.  Same process for 2, except this time we divided by 3.

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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
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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

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Step-by-step explanation:

<u>Part A </u>

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

<u>Part B </u>

<u>(Fixed Cost)</u>

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 .

<u> Marginal Cost Function</u>

If  c=900+300x+25x^2

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

<u>Part C </u>

<u>Profit Function </u>

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

<u> Part D </u>

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.

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I just took the test and C was not the answer !! I will update this if I figure out what it was.

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