Business, 26.03.2021 21:10 jsavagejsavage8596

A baseball team plays in a stadium that holds 54,000 spectators. With the ticket price at $10, the average attendance at recent games has been 21,000. A market survey indicates that for every dollar the ticket price is lowered, attendance increases by 3000. (a) Find a function that models the revenue in terms of ticket price. (Let x represent the price of a ticket and R represent the revenue.) R(x) =
(b) Find the price that maximizes revenue from ticket sales. $
(c) What ticket price is so high that no revenue is generated? $

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Answer from: andrejr0330jr

a) R(x) = 51000 x - 3000 x²

b) When the Revenue is maximum, The price is $ 8.5

c) When No revenue is generated, The price of the ticket is $17

Explanation:

Given - A baseball team plays in a stadium that holds 54,000 spectators. With the ticket price at $10, the average attendance at recent games has been 21,000. A market survey indicates that for every dollar the ticket price is lowered, attendance increases by 3000.

To find - (a) Find a function that models the revenue in terms of ticket price.

(b) Find the price that maximizes revenue from ticket sales.

Proof -

Let us assume that,

The price of a ticket = x

The revenue = R

Now,

Total number of tickets sold , N = 21000 + 3000(10 - x)

= 21000 + 30000 - 3000 x

= 51000 - 3000 x

⇒Total number of tickets sold , N = 51000 - 3000 x

Now,

Revenue , R(x) = x * N

= x [ 51000 - 3000 x ]

= 51000 x - 3000 x²

⇒R(x) = 51000 x - 3000 x²

For maximum Revenue,

Put $\frac{dR(x)}{dx} = 0$

Now,

$\frac{dR(x)}{dx}$ = 51000 - 6000 x

⇒51000 - 6000 x = 0

⇒6000 x = 51000

⇒6x = 51

⇒x = $\frac{51}{6}$ = 8.5

∴ we get

When the Revenue is maximum, The price = $ 8.5

If No Revenue is generated

⇒R(x) = 0

⇒51000 x - 3000 x² = 0

⇒1000 x ( 51 - 3 x ) = 0

⇒1000 x = 0, 51 - 3 x = 0

⇒x = 0, 3 x = 51

⇒x = 0, x = $\frac{51}{3}$

⇒x = 0, x = 17

∴ we get

When No revenue is generated, The price of the ticket is $17

Answer from: Quest

you have to put the parentheses like this:

$(85-4) \div 9 \times 10$

in fact, you have to perform the operation inside parentheses first, and then proceed in order:

$81 \div 9 \times 10 = 9 \times 10 = 90$

Answer from: Quest

Answerradio shack is an example of a franchise;

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