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AnnyKZ [126]
2 years ago
14

The latest demand equation for your gaming website, www.mudbeast.net, is given by

Mathematics
1 answer:
horrorfan [7]2 years ago
7 0

Answer:

C(x) =  $850 - $350x

Monthly Profit =   -500x² + 1550x - 850

x = $1.55

the largest possible monthly profit  = $351.25

Step-by-step explanation:

Given:

Demand equation:

q = -500x + 1200

where, q is the number of users who log on per month

x is the log-on fee you charge

Site maintenance fee =  $10 per month

High-volume access fee =  $0.70 per log-on

Now,

C(x) = $10 + ( $0.70 × q )

or

C(x) = $10 + ( $0.70 × (-500x + 1200) )

or

C(x) = $10 + ( - $350x + 840 )

or

C(x) =  $850 - $350x

Total monthly income = qx

or

Total monthly income = ( -500x + 1200 ) × x

or

Total monthly income = -500x² + 1200x

now,

Profit = Income - cost

or

Monthly Profit =   -500x² + 1200x - ( 850 - 350x )

or

Monthly Profit, P(x) =   -500x² + 1550x - 850

For the largest possible monthly profit

\frac{d\textup{P(x)}}{\textup{dx}} = 0

or

\frac{d(-500x^2+1550x-850)}{\textup{dx}} =0

or

-2 × 500x + 1550 = 0

or

-1000x + 850 = 0

or

x = $1.55

Now,

the largest possible monthly profit will be at x = $1.55

substitute in the function of profit

P(1.55) =   ( -500× 1.55² ) + ( 1550 × 1.55 ) - 850

or

the largest possible monthly profit = - 1201.25 + 2402.5 - 850

or

the largest possible monthly profit  = $351.25

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Below is the graph of f ′(x), the derivative of f(x), and has x-intercepts at x = –3, x = 1 and x = 2. There are horizontal tang
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B. False.  f(x) is decreasing when f'(x) is negative.  So f(x) is decreasing in the intervals x < -3 and 1 < x < 2.

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2 years ago
Kelly price sells college textbooks on commission. She gets 8 % on the first $7500 of​ sales, 16% on the next $7500 of​ sales, a
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Answer:

The commission would be $ 920.

Step-by-step explanation:

Given,

Sales in 1997 ​= $ 9500,

Since, there is a commision of 8 % on the first $ 7500 of​ sales, 16% on the next $ 7500 of​ sales, and 20% on sales over $ 15,000,

If x represents the total sales,

Commission for x ≤ 7500 = 8% of x = 0.08x,

Commission for 7500 < x ≤ 15000 = 8% of 7500 + 16% of (x-7500)

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Commission for 7500 < x ≤ 15000 = 8% of 7500 + 16% of 7500 + 20% of (x-15000)

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= 1800 + 0.20(x-15000)

Thus, the function that shows the given situation,

f(x)=\left\{\begin{matrix}0.08x & x \leq 7500\\ 600+0.16(x-7500) & 7500 < x \leq 15000\\ 1800+0.20(x-15000) & 15000 < x\end{matrix}\right.

Since, 9500 lies between 7500 and 15000,

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f(9500)= 600 + 0.16(9500 - 7500) = 600 + 320 = $ 920

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