Question

When the admission price for a baseball games was $4 per ticket, 40,000 tickets were sold. When the price was raised to $5, only 35,000 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 P(x)=
B) Select the graph of P
C) find the marginal profits when 20,000 tickets were sold and when 40,000 tickets were sold. P'(20,000)= $ Per ticket P'(40,000)= $ Per ticket

Answer 1

Answer and explanation:

A. profit P as a function of x, the number of tickets sold

P(x)= total revenue - total cost

For 40000 tickets at $4

=40000×4-0.10×40000+$95000

=$160000-$99000

=$61000

For 35000 tickets at $5

= 35000×$5-0.10×35000+$95000

= $175000-$98500

= $76500

B. P has a downward slope like a demand curve. Increase in price equal to decrease in profit.

C. P(40000)= $4-$0.10+$95000/40000

= $4-$2.475

= $1.525

Price for 20000 tickets was not stated in question but feel free to use an arbitrary price(price should be higher than that for 35000 tickets and 40000 tickets)