FUNCTIONS

APPLIED PROBLEMS

1.        Suppose that the demand and price for a certain model kitchen gadget are related by  where p is price in pesos and x is demand in thousands.  Find the price for each of the following demands.

a)      0

b)      4

c)       8

d)      Find the demand for each of the following prices A) 6; B) 10; C) 16

e)      Graph

2.       Suppose the price and supply of the item above are related by .  Find the supply when the price is a) 0; b) 10; c) 20; d) graph ; e) find the equilibrium supply; f) find the equilibrium price.

3.       Let the supply and demand functions for a certain kind of licorice be  and  where x is in thousands of pounds and p is in pesos.

a)      Graph these on the same axes.

b)      Find the equilibrium demand

c)       Find the equilibrium price

Let the supply and demand functions for a certain flavor ice cream be given by  where x is in thousands of gallons and p is in pesos.

a)      Graph these on the same axes.

b)      Find the equilibrium demand.

c)       Find the equilibrium price.

A classic study on the supply and demand for sugar produced the following results:

a)      Graph these on the same axes

b)      Find the equilibrium demand.

c)       Find the equilibrium price

4.       In a recent issue of The Busy Journal, we are told that the relationship between x, the amount that an average family spends for food, and y, the amount it spends on eating out, is approximated by the model y =0.36x.  Find y if x is

a)      P40

b)      P80

c)       P120

d)      Graph the function

5.       In an issue of Busy Week, the president of Insta-Tune, a chain of franchised automobile tune-up shops, says that people who buy a franchise and open a shop pay a weekly fee of  to company headquarters.  Here, y is the fee and x is the total amount of money taken in during the week by the tune-up center.  Find the weekly fee if x is

a)      P0

b)      P1000

c)       P2000

d)      P3000

e)      Graph the function

6.       Suppose the sales of a particular brand of electric guitar satisfy the relationship  where S(x) represents the number of guitars sold in year x, with x = 0 corresponding to 1979.  Find the sales in each of the following years.

a)      1981

b)      1982

c)       1983

d)      1979

e)      Find the annual rate of change of the sales

7.       If the population of ants in an anthill satisfies the relationship  where A(x) represents the number of ants present at the end of month x, find the number of ants present at the end of each of the following months.  Let x = 0 represent June

a)      June

b)      July

c)       August

d)      December

e)      What is the monthly rate of change of the number of ants?

8.       Let  represent the number of bacteria (in thousands) present in a certain culture at time x, measured in hours, after an anti-bacterial spray is introduced into the environment.  Find the number of bacteria present at the following times.

a)      X = 0

b)      X = 6

c)       X = 20

d)      What is the hourly rate of change in the number of bacteria?

9.       Jose runs a sandwich shop.  By studying data for his past costs, he has found that a mathematical model describing the cost of operating his shop is given by  where C(x) is the daily cost in pesos to make x dozen sandwiches.

a)      Graph C(x)

b)      Form the vertex of the parabola , find the number of dozen sandwiches Jose must to sell to produce minimum cost.

c)       Find the minimum cost.

10.   Donna runs a “lumpia” stand.  She has found that her profit are approximated by  where P(x) is the profit in hundreds of pesos per month from selling x hundred “lumpia” in a month.

a)      Graph P(x)

b)      Find the number of “lumpia” that Donna should make to produce maximum profit.

c)       What is the maximum profit?