Answered

Westonci.ca is your trusted source for accurate answers to all your questions. Join our community and start learning today! Connect with professionals ready to provide precise answers to your questions on our comprehensive Q&A platform. Our platform offers a seamless experience for finding reliable answers from a network of knowledgeable professionals.

When the admission price for a baseball game was $5 per ticket, 35,000 tickets were sold. When the price was raised to $6, only 30,000 tickets were sold. Assume that the demand function is linear and that the variable and fixed costs for the ball park owners are $0.10 and $95,000 respectively.
(a)
Find the profit P as a function of x, the number of tickets sold

Sagot :

bharathparasad577

The profit function is P(x) = ( - x² / 5000 ) + 11.9x - 95000.

35,000 baseball game tickets were sold at $5 per ticket.

When the price is raised to $6, then 30,000 tickets were sold.

The variable and fixed costs for the ballpark owners are $0.10 and $95,000 respectively.

Let's say x is the number of tickets sold, and P is the profit.

Then,

P = ax + b

At P = 5,

5 = (35000)a + b                                                                                  ---------(1)

At P = 6,

6 = (30000)a + b                                                                                  --------(2)

Subtracting (2) from (1),

5 - 6 = (35000)a + b - (30000)a - b

- 1 = 5000(a)

a = ( - 1/5000)

So if a = ( - 1/5000),

Then,

5 = (35000)a + b

5 = (35000)( - 1 / 5000 ) + b

5 = - 7 + b

b = 12

Therefore,

P(x) = ( - x /5000) + 12

Now, the profit function is:

Profit = Revenue - Costs

P(x) = R(x) - C(x)

Now, R(x) =  xp(x)

R(x) = x[ ( - x/5000) + 12]

R(x) = ( - x² / 5000 ) + 12x

The fixed cost is F(x) = $95000

Hence, the costs will be:

C(x) = 95000 + (0.10)x

Therefore the profit function is:

P(x) = R(x) - C(x)

P(x) = ( - x² / 5000 ) + 12x - 95000 - (0.10)x

P(x) = ( - x² / 5000 ) + 11.9x - 95000

Learn more about profit function here:

https://brainly.com/question/21497949

#SPJ9

We appreciate your visit. Our platform is always here to offer accurate and reliable answers. Return anytime. We appreciate your visit. Our platform is always here to offer accurate and reliable answers. Return anytime. Westonci.ca is committed to providing accurate answers. Come back soon for more trustworthy information.