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3 years ago

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Mathematics

1 answer:

Lerok [7]3 years ago

4 0

Answer:

Huh

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

The selling price of an item is $600. It is marked down by 30%, but this sale price is still marked up

Norma-Jean [14]

Answer:

7000

Step-by-step explanation:

divide 600 and 30 then multiply that answer by 350

7 0

3 years ago

6x7x6x9 this one is for you

Papessa [141]

Answer:HOPE THIS HELPS! :D

2268

Step-by-step explanation:

6x7=42

42x6=252

252x9=2268

so, 6x7x6x9=2268

8 0

3 years ago

What is the value of x?

pantera1 [17]

x=9 because the triangle is equilateral which means every side is equal to 60. When you do the math you get 7x-3=60 which is 7x=63 and 63/7=9

7 0

3 years ago

Read 2 more answers

142 x 12 in algorithm standard and in area model

Katen [24]

Answer:

0333

Step-by-step explanation:

000

0000

1112222

______

11122222 ans

4 0

3 years ago

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