Find the profit function if cost and revenue are given by C(x) = 129 + 1.6x and R(x) = 8x − 0.04x .
2
The profit function is P(x) = − 0.04x + 6.4x − 129 .
2
YOU ANSWERED: − 0.04x − 6.4x − 129
4
1: http://media.pearsoncmg.com/cmg/pmmg_mml_shared/calc_ifigs/IFig4_05Calculus_application_supply_and_dem
Why might the slider not permit a positive slope in the demand equation?
(Use the interactive figure to find your answer. Change the sensitivity of the slider by pressing the Alt key when
moving the slider.) Click here
to launch
the
interactive
figure.1
Choose the correct answer below.
A. As demand goes up price goes up, and the price cannot go too high.
B. As price goes down demand goes down.
C. The slope of a demand equation can never be positive, because if real life demand increased
without bound, then the market would crash.
D. As price goes down demand goes up.
2: http://media.pearsoncmg.com/cmg/pmmg_mml_shared/calc_ifigs/IFig4_05Calculus_application_supply_and_dem
Use the interactive figure to find the equilibrium quantity for a business that has demand equation
p = 10 − 0.5q and supply equation of p = 4q.
(Use the interactive figure to find your answer. Change the sensitivity of the slider by pressing the Alt key when
moving the slider.)
Click here
to launch
the
interactive
figure.2
q =
(Type an integer or decimal rounded to two decimal places as needed.)
8/7/22, 2:59 PM Section 1.8 Homework-Angie Lopez
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*4. Use the information listed below to solve parts a through h.
Suppose that the demand and price for a certain model of a youth wristwatch are related by the following equation
p = D(q) = 16 − 1.25q
where p is the price (in dollars) and q is the quantity demanded (in hundreds). Find the price at each level of demand.
Answer parts a through d.
a. Find the price when the demand is 0 watches.
The price when the demand is 0 watches is $ .
b. Find the price when the demand is 400 watches.
The price when the demand is 400 watches is $ .
c. Find the quantity demanded for the watch when the price is $6.
At a price of $6, the demand is for watches.
d. Graph p = 16 − 1.25q. Choose the correct graph below.
A.
0 20
0
35
q
p
B.
0 20
0
35
q
p
C.
0 20
0
35
q
p
D.
0 20
0
35
q
p
Suppose the price and supply of the watch are related by the following equation
p = S(q) = 0.75q
where p is the price (in dollars) and q is the quantity supplied (in hundreds) of watches. Answer parts e through g.
e. Find the quantity supplied at a price of $0.
At a price of $0, the supply is watches.
f. Find the quantity supplied at a price of $10.
At a price of $10, the supply is about watches.
(Round to the nearest whole number as needed.)
g. Graph p = S(q) = 0.75q on the same axis used to graph p = 16 − 1.25q in part d. Choose the correct graph below.
A.
0 20
0
35
q
p
B.
0 20
0
35
q
p
C.
0 20
0
35
q
p
D.
0 20
0
35
q
p
h. Given that the demand function is p D(q) q and that the supply function is p S(q) q, find the
equilibrium quantity and the equilibrium price.
= = 16 − 1.25 = = 0.75
8/7/22, 2:59 PM Section 1.8 Homework-Angie Lopez
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*5.
6.
The equilibrium quantity is watches.
The equilibrium price is $ .
Let one week’s supply and demand functions for gasoline be given by and , where p is
the price in dollars and q is the number of 42-gallon barrels. (a) Graph these equations on the same axes. (b) Find the
equilibrium quantity. (c) Find the equilibrium price.
p = D(q) = 288 − q
4
3
p = S(q) = q
2
3
(a) Choose the graph of D(q) and S(q).
A.
0 800
0
400
q
p
B.
0 800
0
400
q
p
C.
0 800
0
400
q
p
D.
0 800
0
400
q
p
(b) The equilibrium quantity is barrels.
(c) The equilibrium price is $ .
Let p and C(x) x, where x is the number of garden hoses that can be sold at a price of $p per unit and
C(x) is the total cost (in dollars) of producing x garden hoses.
= 24 − x = 695 + 3
(A) Express the revenue function in terms of x.
(B) Graph the cost function and the revenue function in the same viewing window for Use approximation
techniques to find the break-even points.
0 ≤ x ≤ 576.
(A) R(x) =
(B) Choose the correct graph for R(x) and C(x) on [0, 576] × [0, 2400].
A.
0 200 400
0
600
1200
1800
2400
x
y
B.
0 200 400
0
600
1200
1800
2400
x
y
C.
0 200 400
0
600
1200
1800
2400
x
y
The break-even point on the left is approximately , .
(Round each coordinate to the nearest integer as needed.)
The break-even point on the right is approximately , .
(Round each coordinate to the nearest integer as needed.)
8/7/22, 2:59 PM Section 1.8 Homework-Angie Lopez
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*7. At a price of $ per bushel, the supply of a certain grain is million bushels and the demand is million bushels.
At a price of $ per bushel, the supply is million bushels and the demand is million bushels.
2.25 7500 7800
2.36 7900 7700
(A) Find a price-supply equation of the form p mx b, where p is the price in dollars and x is the supply in millions of
bushels.
= +
(B) Find a price-demand equation of the form p mx b, where p is the price in dollars and x is the demand in millions of
bushels.
= +
(C) Find the equilibrium point.
(D) Graph the price-supply equation, price-demand equation, and equilibrium point in the same coordinate system.
(A) The price-supply equation is p = .
(Type an exact answer. Use integers or decimals for any numbers in the equation.)
(B) The price-demand equation is p = .
(Type an exact answer. Use integers or decimals for any numbers in the equation.)
(C) The equilibrium point is .
(Type an ordered pair. Type an exact answer. Use integers or decimals for any numbers in the expression.)
(D) Choose the correct graph below.