December 09, 2013
6-3
Further Business Applications:
Economic Lot Size;
Economic Order Quantity;
Elasticity of Demand
Variable
q
k
f
M
Lot Size
Order Quantity
# units in a batch
# units to order at a time
cost of storing for 1 year
cost of storing for 1 year
fixed set up cost
amount for a reorder
total # units produced
annually
total # units produced
annually
Example 1
Example 2
A manufacturer has a steady annual demand for 7936 cases of sugar. It
costs $8 to store 1 case for 1 year, $31 in set-up costs to produce each
batch, and $16 to produce each case. Find the number of cases per
batch that should be produced to minimize cost.
A restaurant has an annual demand for 894 bottles of California wine. It
costs $4 to store 1 bottle for 1 year and it costs $7 to place a reorder.
Find the optimum number of bottles per order.
Example 3
Every year, Danielle Santos sells 35,808 cases of her Delicious Cookie
Mix. It costs her $2 per year in electricity to store a case, plus she must
pay annual warehouse fees of $2 per case for the maximum number of
cases she will store. If it costs her $746 to set up a production run, plus
$10 per case to manufacture a single case, how many production runs
should she have each year to minimize her total costs?
If a small change in price is accompanied by a large change in quantity
demanded, the product is said to be elastic (responsive to price
changes)
A product is inelastic if a large change in price is accompanied by a
small amount of change in demand.
Revenue is maximized when the elasticity of demand is equal to 1.
December 09, 2013
Example 4
Example 5
For the following demand function,
find:
a) E
b) the values of q at which total revenue is maximized.
Find the elasticity of demand (E) for the given demand function at the
indicated values of p. Is the demand elastic, inelastic or neither at the
indicated values?
a) $21
b) $36
Example 6
A study of the demand for air travel between two cities depends on the
airfare according to the following demand equation
q = 55.3 - 0.022p
a) Find the elasticity of demand (E) when the price is $166.08
b) Is the demand for airfare elastic or inelastic at this price?
c) Find the price that maximizes revenue.