Due: 19 September 2011
Math 1090-002
09 September 2011
Section 1.6 Homework
Instructions: Complete the following problems in the space provided. Please
show your work; write down enough so that a classmate could follow the steps
you’ve taken to arrive at the solution. You can earn up to 40 points on the
assignment.
Note: The problems have been taken from Section 1.6 in the book, but those
denoted by asterisks (*) have been augmented. You can still check your answers
in the back for all but the extra bits.
9*. [15 points] Fixed costs for a roller skate manufacturer are $400 per day with
a total cost of $4500 per day. Output is 100 pairs of skates per day.
(a) In one sentence, define what is meant by the term “variable costs”. What
are the variable costs per day?
(b) Define marginal cost. What is the marginal cost for a day’s output?
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(c) If a pair of skates is sold to a retailer for $60, write down the revenue
function. What is the manufacturer’s revenue for 200 pairs of skates?
(d) What is the marginal revenue?
(e) What is the manufacturer’s profit from selling 600 pairs of skates? (In the
back of the book, the answer is given as $11,000. I believe that, based on
all of the information given in the problem, the answer is $9000. Can you
explain both of these “answers”?)
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10*. [7 points] A doughnut shop has fixed costs of $175 per day and variable
costs of $0.15 per doughnut.
(a) What is the shop’s total cost function per day?
(b) How many doughnuts can be produced for $500 per day?
(c) If the doughnuts are sold for $0.50 apiece, how many doughnuts must be
sold in a day in order to break even?
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14. [6 points] A craftsman makes and sells leather belts for $15 each. If his
tools and machines required $30 in one-time setup costs and his variable costs
are $9 per belt, how many belts must he sell to break even?
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26*. [9 points] Retailers will buy 45 books from a wholesaler if the price is $10
each, but only 20 books if the price is $60. The wholesaler will supply 35 books
at $30 each and 70 books at $50 each.
(a) Assuming the supply equation is linear, write it down.
(b) Find the demand equation, assuming it too is linear.
(c) Find the market equilibrium point.
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25*. [3 points] Assume supply for a toy is given by 35p − 20q = 350 and demand
by p + 2q = 100. What is the equilibrium point?
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