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2 years ago

5

Find the value of x.6x + 12 3x + 3

1 answer:

Alekssandra [29.7K]2 years ago

6 0

sorry it took a long time

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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

Which systems of equations have no solution?

vlada-n [284]

Answer:

The last block where is says y=13-2x and 4x-y=-1 is the correct answer

I got a 100% in this test. It is right

Plz give brainliest :)

5 0

3 years ago

Read 2 more answers

Can someone plz help me solved this problem! Need help ASAP! Help me !

lana66690 [7]

Answer: 5, 8

<u>Step-by-step explanation:</u>

The difference between 3 times a number and -8 is BETWEEN 23 and 32

Note: "difference" means subtraction --> 3x - (-8) --> 3x + 8

23 < 3x + 8 < 32

15 < 3x < 24 <em> subtracted 8 from all 3 sides</em>

--> 5 < x < 8 <em>divided 3 from all 3 sides</em>

5 0

3 years ago

The table shows the numbers of studeNt at a highschool who take spanish and Chinese. No student take both language what is p (se

Anastaziya [24]

Answer:

the answer is X

Step-by-step explanation:

it is x

6 0

3 years ago

A camera shop purchases a camera for $56.98 and sells it for $102.56. What is the percent of markup?

Amiraneli [1.4K]

Answer:

180%

Step-by-step explanation:

Set up an equation:

Variable x = percent of markup

102.56/56.98 = x/100

Cross multiply

102.56 × 100 = 56.98 × x

10,256 = 56.98x

Divide both sides by 56.98:

179.99297.... = x

Round to nearest whole number:

180 = x

Check your work:

56.98 × 180%

Convert the percentage into a decimal:

56.98 × 1.80

102.564

Round to nearest cent:

102.56

Correct!

8 0

3 years ago