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Unformatted text preview: ceived from the ﬂight. (ii) What is the maximum revenue? 56. A manufacturer has a steady annual demand for 14,850 cases of sugar. It costs $9 to store 1 case for
1 year, $33 in set up cost to produce each batch, and $17 to produce each case. Find the number of
cases per batch that should be produced to minimize cost. 57. A restaurant has an annual demand for 921 bottles of California wine. It costs $1 to store 1 bottle for
1 year, and it costs $9 to place a reorder. Find the optimum number of bottles per order.
The optimum number of bottles per order is
(A) less than 105 (B) between 105 and 115 (D) between 125 and 135 (C) between 115 and 125 (E) more than 135 58. Find the elasticity of demand for the demand function
q = 402 − 0.3p2
for p = $22.
The elasticity of demand for p = $22 is
(A) less than 0.5 (B) between 0.5 and 1.0 (D) between 2.0 and 4.0 (E) more than 4.0 (C) between 1.0 and 2.0 59. The shortterm demand for crude oil in Country A in 2008 can be approximated by
q = f (p) = 1, 615, 368p−.05 ,
where p represents the price of crude oil in dollars per barrel and q represents the per capita consumption
of crude oil. Answer parts (i) and (ii)
(i) What is the elasticity of demand for oil when the price is $96 per barrel?
(A) less than 0.25 (B) between 0.25 and 0.75 (D) between 1.25 and 1.75 (C) between 0.75 and 1.25 (E) more than 1.75 (ii) Interpret the elasticity of demand. Choose the correct answer below.
(A) The demand is elastic, so as price increases, revenue decreases. (B) The demand is elastic, so as price increases, revenue increases. (C) The demand is inelastic, so as price increases, revenue increases. (D) The demand is inelastic, so as price increases, revenue decreases. Formulas You Might Find Useful
I = A=
A= P rt
r mt
P 1+
m
P ert
= rE = er − 1 f ( x) = f ( x + h) − f ( x )
h→0
h d
[f (g (x))]
dx = f (g (x)) · g (x) = u( x) · v ( x) + v ( x) · u ( x) = v ( x) · u ( x) − u( x) · v ( x)
[v (x)]2 dx
[a ]
dx = (ln a)ax d
[loga (x)]
dx = 1
(ln a)x E = q = d
[u(x) · v (x)]
dx
d u( x)
dx v (x) 1+ r m
−1
m rE lim p dq
−·
q dp
2f M
k...
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 Fall '09
 JESS
 Calculus, Derivative

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