Brandon is thinking of two numbers. Their sum is - 10 and their difference is -2.

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

3 years ago

WILL GIVE BRAINLIEST: if the roots of the equation x^3 +px^2+qx+r = 0 are 2, 3, and 4, find the values of p, q, and r.

klasskru [66]

8+4p+2q+r=0
27+9p+3q+r=0
64+16p+4q+r=0
P=-9
Q=26
R=-24

5 0

3 years ago

A newborn child receives a $20,000 gift toward college education from her grandparents. How much will the 20,000 be worth in 17

Alexus [3.1K]

Answer:

The amount the $20.000 will be worth in 17 years at compound interest is $65068.443

Step-by-step explanation:

Here we have the Principal, P = $20,000.00

The annual interest rate, r = 7% = 0.07

Time , t = 17 years

Number of compounding period per year, m = quarterly = 4

The compound interest can be found from the following formula;

$Amount, \ A = P \left (1 + \frac{1}{r} \right )^{mt}$

Therefore, by plugging the values of the equation parameters, we have;

$Amount, \ A = 20000 \left (1 + \frac{0.07}{4} \right )^{4 \times 17} = \$ 65068.443$

Therefore, the amount the $20.000 will be worth in 17 years at compound interest = $65068.443.

7 0

3 years ago

Thanks for help have nice day

kupik [55]

Answer: 6. d

7. b

8. d

9. c

Step-by-step explanation:

8 0

3 years ago

4x + 2y = 8 16x - y = 14

lys-0071 [83]

Equation 1) 4x + 2y = 8
Equation 2) 16x - y = 14

Multiply all of equation 2 by 2.

2) 2(16x - y = 14)

2) 32x - 2y = 28
1) 4x + 2y = 8

Add equations together.

36x = 36

Divide both sides by 36.

x = 1

Plug in 1 for x in the first equation.

4x + 2y = 8

4(1) + 2y = 8

4 + 2y = 8

Subtract 4 from both sides.

2y = 8 - 4

2y = 4

Divide both sides by 2.

y = 4/2

y = 2

So, x = 1, y = 2

~Hope I helped!~

7 0

3 years ago