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Unformatted text preview: AEB 3510: APPLICATIONS OF DERIVATIVES Chapter 10 Supplemental Problems: 1. A toll road averages 35,000 cars per day. Suppose that the Department of Transportation estimates the demand function for the toll‐road to be Q( p) = 60000 − 250 p where Q is the number of cars per day using the toll‐road and p is the toll in cents. a) What out the Total Revenue function for the toll road? b) (b) What is the optimal toll rate that should be charged? (Note: The optimal toll rate is the toll rate that maximizes revenues). 2. A movie theater sells tickets for $8.00 and on Friday evenings, it averages about 720 tickets sold. A survey shows that for each $0.25 drop in ticket price, 20 more people will buy tickets on Friday evenings. a) What is the movie theater’s Total Revenue function? b) What ticket price will maximize Total Revenue? 3. The fish population on Georges Bank in New England has been overharvested. After severe conservation measures in place, the environmental economists expect the fish population to grow according to the following rule: where N (t) denotes the population of fish at the end of year t. a) Find the rate of growth of the fish population 2 years after the implementation of the conservation measures. b) What will the population of the fish be 10 years after the conservation measures are implemented? 4. An efficiency study by Elektra Electronics showed that the number of Space Commander walkie‐ talkies assembled by the average worker t hours after starting work at 8 A.M. is given by: with t=0 representing 8 A.M and t>0 representing each working hour after 8 A.M. (a) Find the rate at which the average worker will be assembling walkie‐talkies t hours after starting work. At what rate will the average working be assembling walkie‐talkies at 10 A.M.? What about 3 P.M.? 5. The relationship between the amount of money, x, that Elektra Electronics spends on advertising and the company’s total sales, S(x), is approximated by the following function: where x is measured in thousands of dollars spent on advertising. a) Find the rate of change of the total sales with respect to the amount of money spent on advertising. b) Are Elektra’s total sales increasing at a faster rate when the amount of money spent on advertising is $100,000 or $150,000? 6. The ordering and transportation cost, C, for the components used in manufacturing walkie‐talkies by Elektra Electronics is estimated as: where C is measured in thousands of dollars and x is the order size in hundreds. a) Find the rate of change of the cost C with respect to the order size x when x=10 and x=15. b) What do these rates of change imply about increasing order size? ...
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This note was uploaded on 02/10/2011 for the course AEB 3510 taught by Professor Mikaelsandberg during the Spring '11 term at University of Florida.
- Spring '11