MATH

Old #1: NY State Electric and Gas charges each residential customer a basic fee of $3.11, plus $0.0347 per kilowatt-hour (kWh).

a. Assuming there are 700,000 residential customers, find the company’s fixed revenue function. This is the amount of money the company collects for all 700,000 customers even if no kilowatt-hours are used.

b. b. Still assuming there are 700,000 residential customers, and assuming those customers use X kilowatt-hours of power, find the function for its total revenue:

R(X) = 2,177,000 + 0.0347x

c. How much does the revenue increase for each additional kilowatt-hour? This is the marginal revenue.

Marginal revenue R’(X)

=0.034

New #1: Your answer to part b defined revenue as a linear function.

a. What is the slope of that linear function, and what is the meaning of slope in this application?

b. What is the y-intercept of that linear function, and what is the real-life meaning of y-intercept in this application?

Old #2: Cal makes calculators. His equipment to make calculators cost him $50. The materials for each calculator he makes cost him $5.

a. What is the function that describes the total cost for Cal to make X calculators?

b. What is the average cost per calculator if Cal makes 100 calculators?

New #2: Consider the linear cost function you found in part a.

a. What is the slope of that linear function, and what is the meaning of slope in this application?

b. What is the y-intercept of that linear function, and what is the real-life meaning of y-intercept in this application?

Old #3: Gerty’s Gadgets can produce 100 gadgets for $1500. Gerty’s marginal costs for each gadget are $10 – this means it costs $10 for Gerty to make each gadget (in addition to her fixed costs).

a. What are Gerty’s fixed costs? This is how much it would cost her to make 0 gadgets.

Of the 100 gadgets produce the total variable costs is 100*$10=$1000. Thus fixed costs is $1,500-1,000=$500

b. What is Gerty’s cost function – the cost for Gerty to create X gadgets:

New #3: Consider the linear cost function you found in part b.

a. What is the slope of that linear function, and what is the meaning of slope in this application?

b. What is the y-intercept of that linear function, and what is the real-life meaning of y-intercept in this application?

Old #4: An electronics company manufactures handheld PCs. The cost function, in dollars, for their top-selling model is C(x) = 160x + 750,000

a. What is the fixed cost for this product?

$750,000

b. What is the marginal cost for this product?

New #4: Relate the concepts of fixed cost and marginal cost to slope and intercept:

Old #5: A company manufactures a particular model of a DVD player that sells to retailers for $168. The cost of making x of these players is given by the function C(x) = 118x + 800,000.

a. Find the revenue function for selling x DVD players to retailers:

b. Find the profit function for selling x DVD players to retailers:

c. What is the profit from selling 100,000 players?

d. What is the marginal revenue from selling an additional DVD player after 10,000 players have been sold?

e. What is the marginal profit from selling an additional DVD player after 10,000 players have been sold?

f. How many players must be sold for the manufacturer to not lose money?

New #5: Relate the concept of break-even point (#f above) to the concept of the intercept of a line.