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Stewart_Calc_7ET ch08sec04
MULTIPLE CHOICE
1. The marginal cost function is defined to be the derivative of the cost function. If the
marginal cost of manufacturing x units of a product is
(measured in dollars per unit) and the fixed start-up cost is , use the Total
Change Theorem to find the cost of producing the first 5,000 units.
a.
$35,454,500
b.
$35,484,500
c.
$35,444,500
d.
$35,434,500
e.
$
2. Dye dilution is a method of measuring cardiac output. If A mg of dye is used and c(t) is the
concentration of the dye at time t, then the cardiac output over the time interval [0, T ] is given
by
Find the cardiac output over the time interval [0, 15] if the dye dilution method is used with
mg of dye and the dye concentration, in mg/L, is modeled by
,
where t is measured in seconds.
a.
0.031
b.
0.043
c.
0.029
d.
0.049
e.
f.
0.022
3. The marginal revenue from producing x units of a certain product is
(in dollars per unit).
Find the increase in revenue if the production level is raised from 1,100 units to units.
a.
$17765250
b.
$
c.
$26866667
d.
$37974583
e.
$51367000
4. The demand function for a commodity is given by
.
Find the consumer surplus when the sales level is .
a.
$10458
b.
$4458
c.
$
d.
$9458
e.
$8458
5. A hot, wet summer is causing a mosquito population explosion in a lake resort area. The
number of mosquitoes is increasing at an estimated rate of per week (where t is
measured in weeks). By how much does the mosquito population increase between the 4th
and th weeks of summer?
a.
b.
7702
c.
5702
d.
6702
e.
8702
NUMERIC RESPONSE
1. A demand curve is given by
.
Find the consumer surplus when the selling price is $ .
2. For a given commodity and pure competition, the number of units produced and the price per
unit are determined as the coordinates of the point of intersection of the supply and demand
curves. Given the demand curve
and the supply curve
,
find the consumer surplus.
3. A movie theater has been charging $ .00 per person and selling about tickets on a
typical weeknight. After surveying their customers, the theater estimates that for every $
that they lower the price, the number of moviegoers will increase by per night. Find the
demand function and calculate the consumer surplus when the tickets are priced at $ .
