Chapter 6 applications of the Derivative
368
6.3 ExErcisEs
1. In the discussion of economic lot size, use the critical point
theorem to show that
21
2ƒM
2
/
k is the economic lot size that
minimizes total production costs.
2. Why do you think that the cost g does not appear in the equa-
tion for q [Equation (3)]?
3. Choose the correct answer. Source: American Institute of
Certied Public Accountants.
The economic order quantity formula assumes that
(a) Purchase costs per unit differ due to quantity discounts.
(b) Costs of placing an order vary with quantity ordered.
(c) Periodic demand for the goods is known.
(d) Erratic usage rates are cushioned by safety stocks.
4. Describe elasticity of demand in your own words.
5. A Giffen good is a product for which the demand function
is increasing. Economists debate whether such goods actu-
ally exist. What is true about the elasticity of a Giffen good?
Source: investopedia.com.
6. What must be true about the demand function if
E=0?
7. Suppose that a demand function is linear—that is,
q=m–np
for
0…p…m
/
n,
where m and n are positive constants. Show
that
E=1
at the midpoint of the demand curve on the interval
0…p…m
/
n;
that is, at
p=m
/
12n2.
8. Suppose the demand function is of the form q
=
Cp
–k
, where C
and k are positive constants.
(a) Find the elasticity E.
13. Order Quantity A bookstore has an annual demand for
100,000 copies of a best-selling book. It costs $0.50 to store
1 copy for 1 year, and it costs $60 to place an order. Find the
optimum number of copies per order.
14. Order Quantity A local juice producer has an annual demand
for 3000 dozens of empty clean bottles. It costs $5 to store 1
dozen empty bottles for 1 year, and it costs $200 to place an order.
Find the optimum number of dozens of bottles per order.
15. Lot Size Suppose that in the inventory problem, the storage
cost depends on the maximum inventory size, rather than the
average. This would be more realistic if, for example, the com-
pany had to build a warehouse large enough to hold the maxi-
mum inventory, and the cost of storage was the same no matter
how full or empty the warehouse was. Show that in this case
the number of units that should be ordered or manufactured to
minimize the total cost is
q=
A
ƒM
k
.
16. Lot Size A book publisher wants to know how many times a
year a print run should be scheduled. Suppose it costs $1000
to set up the printing process, and the subsequent cost per
book is so low it can be ignored. Suppose further that the
annual warehouse cost is $6 times the maximum number of
books stored. Assuming 5000 copies of the book are needed
per year, how many books should be printed in each print run?
(See Exercise 15.)
17. Lot Size Suppose that in the inventory problem, the storage
M07_LIAL8971_11_SE_C06.indd 368 20/08/16 4:34 AM
=
–k
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