Question

For the demand function

q equals Upper D left parenthesis x right parenthesis equals StartFraction 400 Over x EndFractionq=D(x)=400x,

find the following.

a) The elasticity

b) The elasticity at

xequals=77,

stating whether the demand is elastic, inelastic, or has unit elasticity

c) The value(s) of x for which total revenue is a maximum (assume that x is in dollars)

Answer #1

we have

the elasticity of the demand is,

..............a)

put x = 77

.............b)

here E > 1,

the demand is inelastic. ..............c)

E = 1 for the maximum revenue,

.............d)

For the demand function
q equals Upper D left parenthesis p right parenthesis equals 352
minus pq=D(p)=352−p,
find the following.
a) The elasticity
b) The elasticity at
pequals=118118,
stating whether the demand is elastic, inelastic or has unit
elasticity
c) The value(s) of p for which total revenue is a maximum
(assume that p is in dollars)

Given Cost and Price (demand) functions Upper C left
parenthesis q right parenthesis equals 120 q plus 45000 and p left
parenthesis q right parenthesis equals negative 2.1 q plus 900,
what is the marginal revenue when profits are $14000?

For the demand function q=D(p)=500/(p+2)2 , find the
following.
a) The elasticity
b) The elasticity at p=3, stating whether the demand is
elastic, inelastic or has unit elasticity
c) The value(s) of p for which total revenue is a maximum
(assume that p is in dollars)

Market supply and demand for ovens are given by p equals Upper S
left parenthesis q right parenthesis equals 1750 plus 5 q and p
equals Upper D left parenthesis q right parenthesis equals 2500
minus 10 q. The equilibrium price is $2000 per oven.
(a) Find the market surplus up to equilibrium using the
integral definition.
(b) Verify the market surplus by calculating
MSequalsCSplusPS.

A bakery works out a demand function for its chocolate chip
cookies and finds it to be
q equals Upper D left parenthesis x right parenthesis equals 705
minus 10 xq=D(x)=705−10x,
where
qq
is the quantity of cookies sold when the price per cookie, in
cents, is
xx.
Use this information to answer parts a) through
f).
a) Find the elasticity.
E(x)equals=nothing
b) At what price is the elasticity of demand equal to 1?
nothingcents¢
(Round to the nearest cent...

A record club has found that the marginal profit,
Upper P prime left parenthesis x right parenthesisP′(x) ,
in cents, is given by
Upper P prime left parenthesis x right parenthesis equals
negative 0.0008 x cubed plus 0.35 x squared plus 52.9
xP′(x)=−0.0008x^3+0.35x^2+52.9x
for
x less than or equals x≤400 ,
where x is the number of members currently enrolled in the club.
Approximate the total profit when
240 members are enrolled by computing the sum
Summation from i equals...

The cost, in dollars, of producing x belts is given by Upper C
left parenthesis x right parenthesis equals 805 plus 18 x minus
0.075 x squared. The revenue, in dollars, of producing and
selling x belts is given by Upper R left parenthesis x right
parenthesis equals 31 x Superscript six sevenths . Find the rate at
which average profit is changing when 676 belts have been produced
and sold. When 676 belts have been produced, the average profit...

Suppose that Upper X has a discrete uniform distribution f
left-parenthesis x right-parenthesis equals StartLayout
left-brace1st Row 1st Column 1 divided by 3, 2nd Column x equals
1,2,3 2nd Row 1st Column 0, 2nd Column otherwise EndLayout A random
sample of n equals 35 is selected from this population. Find the
probability that the sample mean is greater than 2.1 but less than
2.6. Express the final answer to four decimal places (e.g. 0.9876).
The probability is

Find the absolute maximum and absolute minimum for f left
parenthesis x right parenthesis space equals space fraction
numerator x over denominator x squared minus x plus 1 end fraction
on the closed interval between 0 and 3

Estimate the area under the graph of f left parenthesis x right
parenthesis equals 5 x cubed f(x)=5x3 between x equals 0 x=0 and x
equals 1 x=1 using each finite approximation below. a. A lower sum
with two rectangles of equal width b. A lower sum with four
rectangles of equal width c. An upper sum with two rectangles of
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