Michael has 594 friends and 8 pies. How many pieces will each friend get?

An aircraft manufacturer wants to determine the best selling price for a new airplane. The company estimates that the initial co

Blizzard [7]

Answer:

$(a)$ $C(x)=500+20x-5x^{\frac{3}{4}}+0.01x^2$

$p(x)=320-7.7p$

$R(x)=(320-7.7p)p=320p-7.7p^2$

$(b)$ $x=82 \text{planes}$

$(c)$ $p=\$30.91 M\;\; \text{per plane}$

$(d)$ maximum profit $=\$ 15.90M$

Step-by-step explanation:

Given that,

The company estimates that the initial cost of designing the aeroplane and setting up the factories in which to build it will be 500 million dollars.

The additional cost of manufacturing each plane can be modelled by the function.

$m(x)=20x-5x^{\frac{3}{4}}+0.01x^2$

$(a)$ Find the cost, demand (or price), and revenue functions.

$C(x)=500+20x-5x^{\frac{3}{4}}+0.01x^2$

$p(x)=320-7.7p$

$R(x)=(320-7.7p)p=320p-7.7p^2$

$(b)$ Find the production level that maximizes profit.

$f=R(x)-C(x)$

$\Rightarrow f=320p-7.7p^2-(500+20x-5x^{\frac{3}{4}}+0.01x^2)$

$\Rightarrow df=320dp-15.4pdp-20dx+5(\frac{3}{4} )x^{\frac{-1}{4} }dx-0.02xdx$

$x=320-7.7p$

$p=\frac{320-x}{7.7}$

$\frac{dp}{dx} = \frac{-1}{7.7}$

$\frac{df}{dx}=\frac{320}{-7.7} -\frac{15.4(320-x) }{7.7(\frac{-1}{7.7} )}-20+5\frac{3}{4} x^{\frac{-1}{4}} -0.02x=0$

$\Rightarrow -41.5584+83.1169-0.2597x-20+3.75x^{\frac{-1}{4} }-0.02x=0$

$\Rightarrow 21.5585+3.75x^{\frac{-1}{4} }-0.279x=0$

$\Rightarrow x=82 \text{planes}$

$(c)$ Find the associated selling price of the aircraft that maximizes profit.

$p=\frac{320-82}{7.7}$

$\Rightarrow p=\$30.91 M\;\; \text{per plane}$

$(d)$ Find the maximum profit.

Manufacturing cost of one plane is:

$m(1)=20-5+0.01$

$=\$15.01 M$

maximum profit $=\$(30.91-15.01)M$

$=\$15.90M$

3 0

2 years ago

A nutrition laboratory wants to construct a 95% confidence interval for the mean sodium content of "reduced sodium" hot dogs. A

tatuchka [14]

Answer:

n > 96

Therefore, the number of samples should be more than 96 for the width of their confidence interval to be no more than 10mg

Step-by-step explanation:

Given;

Standard deviation r= 25mg

Width of confidence interval w= 10mg

Confidence interval of 95%

Margin of error E = w/2 = 10mg/2 = 5mg

Z at 95% = 1.96

Margin of error E = Z(r/√n)

n = (Z×r/E)^2

n = (1.96 × 25/5)^2

n = (9.8)^2

n = 96.04

n > 96

Therefore, the number of samples should be more than 96 for the width of their confidence interval to be no more than 10mg

6 0

3 years ago

In a school contest, each student draws a number from 1 to 5 out of a large basket. The outcomes are shown in the table below.

12345 [234]

Answer:

The answer is 88/407

Step-by-step explanation:

Their are 5 possible outcomes 1/83, 2/79, 3/88, 4/72, and 5/85. Trust me its 88/407

4 0

2 years ago

Read 2 more answers

The perimeter of a square is equal to four times the length of a side. Write the direct v variation equation that represents the

sveticcg [70]

Answer: $y=4x$

Step-by-step explanation:

A direct variation equation has the form:

$y=kx$

Where k is a constant.

By definition, we know that the perimeter of the square is the sum of the lengths of its sides or, as all the sides are equal, you can multiply the lenght of any side by 4.

Then, knowing that y is the dependent value and x the independent value and the constant k=4, you can write the following direct variation equation that represents the situation.

$y=4x$

4 0

3 years ago

You start driving east for 12 miles, turn left, and drive north for another 10 miles. At the end of driving, what is your straig

Mila [183]

Answer:

15.6=c

Step-by-step explanation:

(12)^2+(10)^2=c^2

144+100=c^2

244=c^2

square root of both sides=244= square root c^2

15.620499=c

15.6=c

6 0

2 years ago

Read 2 more answers