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joja [24]
2 years ago
14

Sales Hester sells televisions. She earns a fixed amount for each television and an additional $20 if the buyer gets an extended

warranty. If Hester sells 15 televisions with extended warranties, she earns $1,500. How much is the fixed amount Hester earns for each television? The fixed amount Hester earns for each television she sells is ​
Mathematics
1 answer:
Butoxors [25]2 years ago
8 0

Answer:

$80

Step-by-step explanation:

15(x+20) = 1500

15x + 300 = 1500

Subtract 300 from each side

15x = 1200

Divide each side by 15

x = 80

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Answer:

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Answer:

The maximum revenue is 16000 dollars (at p = 40)

Step-by-step explanation:

One way to find the maximum value is derivatives. The first derivative is used to find where the slope of function will be zero.

Given function is:

R(p) = -10p^2+800p

Taking derivative wrt p

\frac{d}{dp} (R(p) = \frac{d}{dp} (-10p^2+800p)\\R'(p) = -10 \frac{d}{dp} (p^2) +800 \ frac{d}{dp}(p)\\R'(p) = -10 (2p) +800(1)\\R'(p) = -20p+800\\

Now putting R'(p) = 0

-20p+800 = 0\\-20p = -800\\\frac{-20p}{-20} = \frac{-800}{-20}\\p = 40

As p is is positive and the second derivative is -20, the function will have maximum value at p = 40

Putting p=40 in function

R(40) = -10(40)^2 +800(40)\\= -10(1600) + 32000\\=-16000+32000\\=16000

The maximum revenue is 16000 dollars (at p = 40)

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