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Handout Ch 10 Solutions - AEB 3510 Chapter 10 Supplemental...

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AEB 3510 Chapter 10: Supplemental Problems ANSWER KEY 1. Solution: a) The Total Revenue function for the toll road is given by b) We want to maximize revenues: The revenue function must be concave in order to be maximized: 2 2 ( ) 500 0 d R p dp Hence, the optimal toll rate is $1.20. 2. Solution: Let x = the number of 25 cents reduction in ticket price. The revenue from movie sales is: ( ) (8 0.25 )(720 20 ) TR x x x Note that both the ticket price and the number of customers are a function x since it is the reduction in the ticket price that brings in the 20 additional customers. 2 ( ) 5760 20 5 TR x x x . ( ) 20 10 0 dTR x x dx , x = 2. Ticket price Number of customers
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The revenue function must be concave in order to be maximized: 2 2 ( ) 10 0 d TR x dx Therefore, the movie theater should reduce the ticket price by 50 cents to maximize revenue. 3. Solution: (a) The rate of growth of the fish population at time t is given by: Two years after the implementation of the conservation measures (t=2), the rate of growth of the fish population is:
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