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Ray Of Light [21]

2 years ago

8

An online music store sells about 4000 songs each day when it charges $1 per song. For each $0.05 increase in price, about 80 fe

wer songs per day are sold. Use the verbal model and quadratic function to determine how much the store should charge per song to maximize daily revenue. R(x)=(1+0.05x)(4000-80x)

2 answers:

Anna71 [15]2 years ago

8 0

X is the number of $0.05 price increases
<span>so </span>
<span>15 × 0.05 = $0.75 </span>
<span>and so, walla, (0.75, 4900) </span>
<span>or </span>
<span>increase price by $0.75 for max profit of $4900. </span>

<span>otherwise your math was sound</span>

Shkiper50 [21]2 years ago

5 0

Answer:

The best price is $1.75.

Step-by-step explanation:

Profit = Songs x Price

Given equation is ;

$R(x)=(1+0.05x)(4000-80x)$

Solving this :

Let the number of $0.05 increases be x.

R(x) = $-4x^{2}+120x+4000$

The revenue is maximized when dR/dx = 0.

dR/dx = $-8x+120$

The revenue is maximized when x = 15

Means when the price per song = $1.00 + ($0.05*15) = $1.75

Therefore, the best price is $1.75.

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Step-by-step explanation:

The diagram illustrating the question is shown on the first uploaded image

From the question we are told that

The distance from city A to B is AB = 467.3 miles

The bearing from B to C is $\theta_{BC} = N 28.7E$

The bearing from B to A is $\theta_{BA} = N 60.7E$

The bearing from A to B is $\theta_{AB} = S60.7W$

The bearing from A to C is $\theta_{AC} = S79.1W$

Generally from the diagram

$\theta_A = 180 - 60.7 -79.1$

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Also

$\theta_B = 32^o$

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$\theta_C = 180 - (\theta_A +\theta_B )$

=> $\theta_C = 180 - (40.2 + 32 )$

=> $\theta_C = 107.8 ^o$

Generally according to Sine Rule

$\frac{BC}{sin (\theta_A)} = \frac{CA}{sin (\theta_B)} =\frac{AB}{sin (\theta_C)}$

=> $\frac{BC}{sin (40.2)} = \frac{CA}{sin (32)} =\frac{467.3 }{sin (107.8)}$

So

$\frac{BC}{sin (40.2)} = \frac{467.3 }{sin (107.8)}$

=> $BC = 316.8 \ miles$

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$\frac{CA}{sin (32)} = \frac{467.3 }{sin (107.8)}$

$CA = 260 .1 \ miles$

Generally the additional flyer miles that Adam will receive if he takes the connecting flight rather than the direct flight is mathematically represented as

$k = [CA +BC] - AB$

=> $k = [260 .1 +316.8]- 467.3$

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