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math homework

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. 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) = _______________________________________________________
c. How much does the revenue increase for each additional kilowatt hour? This is the marginal revenue.
2. Cal makes calculators. His equipment to make calculators cost him $50. The materials for each calculator he makes cost him
a. What is the function that describes the total cost for Cal to make X calculators?
C(X) = _______________________________________________________
b. What is the average cost per calculator if Cal makes 100 calculators? 
3. Gerty’s Gadgets can produce 100 gadgets for $1500. Gerty’s marginal costs for each gadget made $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.
b. What is Gerty’s cost function – the cost for Gerty to create X gadgets:
C(X) = _______________________________________________________
c. If Gerty manufactures 100 gadgets, again, we know the total costs are $1500. What is the resulting average cost
per gadget?
d. Use your answer to part b top determine the average cost per gadget if Gerty makes 1000 gadgets instead of 100

4. An electronics company manufactures handheld PCs. The cost function, in dollars, for their top selling model is
750,000 + ݔ160 = (ݔ)ܥ
a. What is the fixed cost for this product?
b. What is the marginal cost for this product?
c. What is the total cost of producing 50,000 handheld PCs?
d. After producing 50,000 units, what is the cost of producing cone more unit? 

5. A company manufactures a particular model of a DVD player that sells to retailers for $168. The cost of making ݔ of these
players is given by the function ܥ(ݔ) = 118 ݔ + 800,000.
a. Find the revenue function for selling ݔ DVD players to retailers:
 _____________________________________________________________ = (ݔ)ܴ
b. Find the profit function for selling ݔ DVD players to retailers:
 _____________________________________________________________ = (ݔ)ܲ
c. What is the profit from selling 100,000 players?
d. What is the marginal revenue from selling an additional DVD player after 100,000 players have been sold?
e. What is the marginal profit from selling an additional DVD player after 100,000 players have been sold?
f. How many players must be sold for the manufacturer to not lose money? 

6. For a certain magazine, the cost function, in dollars, is ܥ(ݔ) = 0.70 ݔ + 1200, where ݔ is the number of magazines sold.
Suppose the magazine sells for $1 a copy. What is the break even point? 

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