Applied business math

Applied business math

Applied business math homework problems on applications of indefinite integrals and definite integrals.

provide step by step solutions

Current Score : 4 / 35 Due : Tuesday, May 9 2017 11:00 PM PDT
1. 1/1 points | Previous Answers
If the marginal revenue (in dollars per unit) for a month is given by what is the
total revenue from the production and sale of 80 units?
$ 31360
2. 2/2 points | Previous Answers
The DeWitt Company has found that the rate of change of its average cost for a product is shown below
where q is the number of units and cost is in dollars.
The average cost of producing 4 units is $56.00.
(a) Find the average cost function for the product.
=
14q+100q+30
(b) Find the average cost of 70 units of the product. (Round your answer to two decimal places.)
$ 48.93
3. 0/1 points | Previous Answers
Suppose that the marginal revenue from the sale of q units of a product is What is
the total revenue in dollars from the sale of 100 units of the product? (Round your answer to the nearest
cent.)
$ 12284.58
Math 112 Section 12.4 (Homework)
WEI TING LEE
Math 112, section A, Spring 2017
Instructor: Ebru Bekyel
WebAssign
MR(q) = -0.2q + 400,
AC'(q) = – 1
4
100
q2
AC(q)
MR(q) = 9e0.04q.
Text
4. 1/3 points | Previous Answers
In the following q is in Items and MC and MR are in dollars per Item.
A firm that sells Items knows that marginal cost is marginal revenue is
and the total cost to produce 100 Items is $12,160.
(a) Find the production level that maximizes profit.
6 Items
(b) Find the profit function.
(c) Find the maximum possible profit.
$
5. –/2 points
You sell Things. Here, marginal revenue and marginal cost are in dollars per Thing and q is in Things.
Suppose that the marginal revenue for a product is and the marginal cost is
with a fixed cost of $700.
(a) Find the profit or loss from the production and sale of 5 Things.
$
(b) How many Things will result in a maximum profit?
units
MC(q) = 2q + 20,
MR(q) = 68 – 6q,
P(q) =
48q-4q2-2140
MR(q) = 2700
MC(q) = 90 q + 4,
6. –/2 points
The average cost for selling q Objects changes at the rate
and the average cost of 5 Objects is $14.00.
(a) Find the average cost function.
(b) Find the average cost of 16 Objects. (Round your answer to the nearest cent.)
$ per Object
7. –/4 points
The marginal cost, in dollars per Framit, for producing q thousand Framits is
The total revenue, in thousands of dollars, for selling q thousand Framits is
(a) Fixed Costs are 100 thousand dollars, find the formula for total cost, in thousands of dollars.
(b) Find the quantity that maximizes profit.
q= thousand Framits
(c) What is the largest possible profit? Include units.
maximum profit =
(d) What quantity will yield the largest total revenue? (Give your answer to the nearest whole Framit.)
Framits
AC'(q)= -5q-2 + 1
5
AC(q) =
MC(q)=3q2-30q+79.
TR(q)=- q2+55q. 3
2
TC(q)=
8. –/11 points
Water is flowing into and out of two vats, Vat A and Vat B. The amount of water, in gallons, in Vat A at
time t hours is given by a function and the amount in Vat B is given by . The two vats contain
the same amount of water at You have a formula for the rate of flow for Vat A and the amount
in Vat B:
Vat A rate of flow:
Vat B amount:
(a) Find all times at which the graph of has a horizontal tangent and determine whether each gives
a local maximum or a local minimum of
smaller t= gives a —Select—
larger t= gives a —Select—
(b) Let Determine all times at which has a horizontal tangent and determine
whether each gives a local maximum or a local minimum. (Round your times to two digits after the
decimal.)
smaller t= gives a —Select—
larger t= gives a —Select—
(c) Use the fact that the vats contain the same amount of water at t=0 to find the formula for the
amount in Vat A at time t.
(d) At what time is the water level in Vat A rising most rapidly?
t= hours
(e) What is the highest water level in Vat A during the interval from t=0 to t=10 hours?
gallons
(f) What is the highest rate at which water flows into Vat B during the interval from t=0 to t=10 hours?
gallons per hour
(g) How much water flows into Vat A during the interval from t=1 to t=8 hours?
gallons
9. –/9 points
The instantaneous speeds for two rocket cars are given by
where t is in minutes and speeds are in miles per minute. Let and represent the respective
distances traveled for the two cars. Since we measure distance traveled from t=0, you may assume that
A(t) B(t)
t=0.
A'(t)=-3t2+24t-21
B(t)=-2t2+16t+40
A(t)
A(t).
D(t)=B(t)-A(t). D(t)
A(t),
A(t)=
a(t)=t2-8t+18 and b(t)=-2t+13,
A(t) B(t)
A(0)=0 and B(0)=0.
(a) Give the formulas for distance traveled.
(b) Find the time in the first ten minutes when Car B is ahead of Car A by the greatest distance and
determine that distance.
t= minutes
greatest distance: miles (Round to two digits after the decimal.)
(c) Determine the lowest speed at which Car A ever travels. Include units.
(d) Write an equation that you would solve in order to find the times when one car passes the other. Put
your equation in the form where
0=
(e) Determine two times at which Car A is traveling at a rate of 8 miles per minute. (Round to two digits
after the decimal.)
earlier time: minutes
later time: minutes
(f) How far does Car B travel during the time interval from t=2 to t=8? Include units.
A(t)=
B(t)=
0=Pt3+Rt2+St+U, P>0.
Current Score : – / 51 Due : Tuesday, May 9 2017 11:00 PM PDT
1. –/12 points
The graph of a function is shown below.
(a) Compute the value of the following definite integrals.
(i)
(ii)
(iii)
(iv)
Math 112 Section 13.2 (Homework)
WEI TING LEE
Math 112, section A, Spring 2017
Instructor: Ebru Bekyel
WebAssign
f(x)
f(x) dx=
2
0
f(x) dx=
3
1
f(x) dx=
8
5
f(x) dx=
6
3
9
(v)
Define a new function
(b) Compute the following values of A.
(i)
(ii)
(iii)
(iv)
(c) At what value of m does A(m) change from increasing to decreasing?
m=
(d) At what value of m does A(m) change from decreasing to increasing?
m=
(e) Compute the largest value of on the interval from m=0 to m=10.
2. –/14 points
The altitude, in feet, of a hot-air balloon at time t minutes is given by a function The graph below
shows the balloon’s rate of ascent at time t. The rate of ascent is given by the function
f(x) dx=
9
6
A(m)= f(x) dx.
m
0
A(0)=
A(2)=
A(5)=
A(6)=
A(m)
A(t).
r(t).
(a) Name all times in the first 10.5 minutes at which the graph of has horizontal tangents.
earlier time: minutes
later time: minutes
(b) Name all times at which the graph of has horizontal tangents.
earlier time: minutes
later time: minutes
(c) Give the time in the first ten minutes when the balloon is highest.
minutes
(d) Find the two-minute interval during which the balloon gains the most altitude. Give the starting time
of that interval.
interval starts at t=
(e) Give the longest interval over which the balloon is rising and getting slower.
from t= to t=
(f) Give the longest interval over which the balloon is falling and getting slower.
from t= to t=
(g) Give the longest interval on which the graph of is concave down.
from t= to t=
r(t)
A(t)
A(t)
(h) How much altitude does the balloon gain from t=11 to t=14? Include units.
(i) What is the average rate of ascent of the balloon during the first three minutes?
feet per minute
3. –/1 pointsHarMathAp10 13.2.001.
Evaluate the definite integral.
4. –/1 pointsHarMathAp10 13.2.005.
Evaluate the definite integral.
5. –/1 pointsHarMathAp10 13.2.009.
Evaluate the definite integral.
8x dx
3
0
x3 dx
4
2
(15 – 6x) dx
4
1
6. –/1 pointsHarMathAp10 13.2.011.
Evaluate the definite integral.
7. –/1 pointsHarMathAp10 13.2.023.
Evaluate the definite integral.
8. –/1 pointsHarMathAp10 13.2.025.
Evaluate the definite integral.
9. –/1 pointsHarMathAp10 13.2.027.
Evaluate the definite integral.
(4×3 – 6×2 – 7x) dx
4
2
dy
2 4
y2 1
e3x dx
3
0
dz
e 7
z 1
10.–/3 pointsHarMathAp10 13.2.037.
Consider the following.
(a) Write the integral that describes the area of the shaded region.
(b) Find the area.
f(x) = 4x – x 1 2
3
dx
0
11.–/2 pointsHarMathAp10 13.2.039.
Consider the following.
(a) Write the integral that describes the area of the shaded region.
(b) Find the area.
y = x3 + 1
dx
0
-1
12.–/2 pointsHarMathAp10 13.2.053.
The rate of depreciation of a building is given by D'(t) = 3000(12 – t) dollars per year, 0 = t = 12; see
the following figure.
(a) Use the graph, and the trapezoid method, to find the total depreciation of the building over
the first 6 years (t = 0 to t = 6).
$
(b) Use the definite integral to find the total depreciation over the first 6 years.
$
13.–/2 pointsHarMathAp10 13.2.055.
A store finds that its sales revenue changes at a rate given by
where t is the number of days after an advertising campaign ends and
(a) Find the total sales for the first week after the campaign ends
$
(b) Find the total sales for the second week after the campaign ends
$
S'(t) = -30t2 + 360t dollars per day
0 = t = 30.
(t = 0 to t = 7).
(t = 7 to t = 14).
14.–/1 pointsHarMathAp10 13.2.058.
Suppose that a vending machine service company models its income by assuming that money flows
continuously into the machines, with the annual rate of flow given by the following formula, in thousands
of dollars per year.
Find the total income from the machines over the first 2 years. (Round your answer to the nearest
thousand dollars.)
thousand dollars
15.–/8 points
The function is given by the formula:
(a) Determine all values of m at which has a local optimum.
local maximum at m=
local minimum at m=
(b) Determine the global maximum and global minimum values of on the interval 0 to 15.
global maximum =
global minimum =
(c) Now suppose that is another function given by the formula and suppose
we plot and on the same axes. Determine the value of m in the interval from 0 to 15 at
which the difference is greatest.
m=
(d) Give the longest interval starting at 0 over which both functions and are increasing.
from m=0 to m=
(e) Give the lowest value of over the interval from m=0 to m=15.
(f) Give the highest value of over the interval from m=0 to m=15.
f(t) = 100e0.02t
F(m)
F(m) = (x2-18x+72) dx.
m
0
F(m)
F(m)
G(m) G(m)=-2m2+48m,
F(m) G(m)
G(m)-F(m)
F(m) G(m)
F'(m)
G(m)