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Amr Nadrah TLenhart 119 Assignment Homework Set 3 due 09/06/2015 at 08:00am MST

1. (1 pt) You want to choose one long distance telephone company from the following options:

Company A charges $0.3 dollars per minute (no fixed monthly charge). Company B charges $13.7 per month plus $0.18 per minute. Company C charges a fixed rate of $50 per month.

Let A(x), B(x), and C(x) denote the monthly charges of Com- pany A, B, and C respectively for spending x minutes on long distance calls.

(a) Find a formula for the monthly cost of using Company A, A(x): A(x) =

(b) Find a formula for the monthly cost of using Company B, B(x): B(x) =

(d) If you spend 125 minutes talking long distance in a month, which of the three companies will be cheapest? Enter the letter (A, B, or C) here:

(e) Given the graph below, match the number of each graph to corresponding company it represents:

Company A Company B Company C

Answer(s) submitted: • 0.3x • 13.7+0.18x • 50 • B

• 1 • 2 • 3

(correct)

2. (1 pt) The linear function y = 2x+28 models the average cost of a haircut in a certain city, where y, is the average price of a haircut x years after 2000. Find the slope for the model. Then describe what this means in terms of the rate of change in the average cost of a haircut over time.

a) m = b) The average cost of a haircut in this city (Enter: in-

creased or decreased or not changed ) at a rate of per year after 2000.

Answer(s) submitted:

• 2 • 30 • 2

(score 0.3333333432674408)

3. (1 pt) An important application of systems of equations arises in connection with supply and demand. As the price of a product increases, the demand for that produce decreases. How- ever, at higher prices, suppliers are willing to produce greater quantities of the product. Suppose a chain of electronics stores sells hand-held color televisions. The weekly demand and sup- ply models are given as follows

Demand model: N =−6p+3036 Supply model: N = 3.2p

where N is the number of televisions sold each week and at price p. (Note: Answer with the appropriate units.)

a) How many hand-held color televisions can be sold at $ 320 per television? Answer:

b) How many televisions will be sold when supply and de- mand are equal? Answer:

c) Find the price at which supply and demand are equal. Answer:

Answer(s) submitted:

• 1024 • 1056 • 330

(score 0.3333333432674408)

4. (1 pt) This table shows the cost of renting a kayak.

The cost of renting a kayak is represented by the equation y = 8x+5., where x represents the number of hours.

What does the slope of the equation represent

• A. the cost of renting a kayak for 8 hours • B. the cost increase for each hour of rental • C. the total cost of the rental • D. the cost of renting a kayak for 5 hours

Answer(s) submitted:

• B

(correct)

5. (1 pt) A gas station sells 1600 gallons of gasoline per hour if it charges $ 2.65 per gallon but only 900 gallons per hour if it charges $ 2.85 per gallon. Assuming a linear model

(a) How many gallons would be sold per hour of the price is $ 2.75 per gallon? Answer:

(b) What must the gasoline price be in order to sell 1400 gal- lons per hour? Answer: $

(c) Compute the revenue taken at the four prices mentioned in this problem – $ 2.65, $ 2.75, $ 2.85 and your answer to part (b). Which price gives the most revenue? Answer: $

(d) What is the price that the gas station should charge to maximize revenue? Answer: $

Answer(s) submitted:

• 1250 • 2.70 • 2.65 • 2.65

(score 0.5)

6. (1 pt) Max Well, a junior college student, lost his scholar- ship after receiving a D in his ”Introductory Electromagnetics” course. He decided to buy a fiddle and make some money as a street musician. His fine instrument cost him $1032.50. Max is a very passionate player and on average he breaks 1 string each hour. He can buy strings for $1.25 each. Find the cost function C(x) associated with Max playing the fid- dle for x hours. C(x) = If on average he makes $16.00 per hour write the revenue func- tion R(x) for the amount of revenue gained from x hours of play- ing. R(x) = Find the profit function P(x) for the amount of profit gained from x hours of playing. P(x) = How many hours will Max need to work to break even? hours

Answer(s) submitted: • 1.25x • 16x • 14.75x •

(score 0.25)

7. (1 pt) It costs a beekeeper $2 to make each pint jar of honey, and

she sells the jars to stores at a price of $3.15 each. Her other monthly costs are the lease of the land and building $740, gen- eral supplies and equipment $180, utilities $330, transportation $190 and fixed salaries $5000 . What is the monthly break even point for the number of pints made and sold to the nearest integer?

The beekeeper decides to give herself a raise amounting to $60 per month. What is the monthly break even point to the nearest integer after the change?

Answer(s) submitted: • 5600 • 7475

(score 0.5)