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A store uses the expression –2p 50 to model the number of backpacks it sells per day, where the price, p, can be anywhere from $9 to $15. Which price gives the store the maximum amount of revenue, and what is the maximum revenue? (Revenue = price mc023-1. Jpg number of backpacks. ) $9. 00 per backpack gives the maximum revenue; the maximum revenue is $32. 0. $12. 00 per backpack gives the maximum revenue; the maximum revenue is $312. 0. $12. 50 per backpack gives the maximum revenue; the maximum revenue is $312. 50. $15. 00 per backpack gives the maximum revenue; the maximum revenue is $20. 0.

Respuesta :

ashishdwivedilVT

By maxima and minima concept, p = $12.50 gives the maximum revenue as $312.50

Expression to model number of backpacks = -2p + 50

As we know that

Revenue collected = Price of a backpack * Number of backpacks

If price  = $9

Number of backpacks = -2*9+50 = 32

Revenue collected = 9 * 32 = 288

If price  = $10

Number of backpacks = -2*10+50 = 30

Revenue collected = 10*30 = 300

If price = $11

Number of backpacks = -2*11+50 = 28

Revenue collected = 11 *28 = 308

If price = $12

Number of backpacks = -2*12+50 = 26

Revenue collected = 12* 26= 312

If price = $13

Number of backpacks = -2*13+50 = 24

Revenue collected = 13 * 24= 312

Since revenue at p=12 and p=13 is the same, it means by the first derivative principle max revenue will be at an average of  points p=12 and p=13

Average value = (12+13)/2 = 12.5

What is first derivative principle?

It says that if we get the maximum value at a point, the function value at the same distance in its neighborhood will be equal.

Revenue at p=12.5:

12.5* [-2*12.5+50] = 312.5

Therefore, p = $12.50 gives the maximum revenue as $312.50.

To get more about derivatives visit:

https://brainly.com/question/22068446

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