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mathematics
mathematical applications for the management

Mathematical Applications For The Management, Life And Social Sciences 12th Edition Ronald J. Harshbarger, James J. Reynolds - Solutions

Dr. Paul Siple conducted studies testing the effect of wind on the formation of ice at various temperatures and developed the concept of wind chill, which we hear reported during winter weather reports. In 2001, the National Weather Service introduced the new wind chill index given in the table.
Suppose a company has the Cobb-Douglas production function z = 300x2/3y1/3 where x is the number of units of labor, y is the number of units of capital, and z is the units of production. Suppose labor costs are $50 per unit, capital costs are $50 per unit, and total costs are limited to
The following table gives the U.S. national consumption and disposable income (both in billions of dollars) for presidential election years from 2012 and projected to 2040.(a) Use linear regression to find the linear equation that is the best fit for these data, with y representing the disposable
In Problem, the demand functions for qA and qB units of two related products, A and B, are given. Complete parts (a)–(e) for each problem. Assume that pA and pB are in dollars.(a) Find the marginal demand of qA with respect to pA.(b) Find the marginal demand of qA with respect to pB.(c) Find the
In Problem, the demand functions for qA and qB units of two related products, A and B, are given. Complete parts (a)–(e) for each problem. Assume that pA and pB are in dollars.(a) Find the marginal demand of qA with respect to pA.(b) Find the marginal demand of qA with respect to pB.(c) Find the
In Orlando, Florida, the following represent the average daily temperatures and humidities for August. Maximum: 91.6°F with 60% humidity Minimum: 73.4°F with 92% humidity Calculate the Summer Simmer Index S and the Apparent Temperature A for both the average daily maximum and the average daily
In Dallas, Texas, the following represent the average daily temperatures and humidities for July. Maximum: 97.8°F with 44% humidity Minimum: 74.7°F with 80% humidity Calculate the Summer Simmer Index S and the Apparent Temperature A for both the average daily maximum and the average daily minimum
One method traffic planners use to calculate recommended curve speeds for trucks is with the formulawhere S is the recommended curve speed in mph, R is the radius of the curve (in feet), V is the average truck speed on the straight approaching the curve (in mph), and B is the banking of the curve
In Problem, evaluate each function as indicated.f (w, x, y, z) = wx - yz2/xy - wz; find f (2, 3, 1, -1).
In Problem, evaluate each function as indicated.w(x, y, z) = x2 + 4yz/xyz; find w(1, 3, 1).
In Problem, evaluate each function as indicated.z(x, y) = x ln y - y ln x; find z(1, 1).
In Problem, find each function’s relative maxima, relative minima, and saddle points, if they exist.z = x3 + y3 - 12x - 27y
In Problem, evaluate each function as indicated.f (x, y) = ln(xy)/x2 + y2 ; find f (-3, -4).
In Problem, find each function’s relative maxima, relative minima, and saddle points, if they exist.z = 16 - x2 - xy - y2 + 24y
In Problem, evaluate each function as indicated.f (x, y) = ye2x + y2; find f (0, 7).
In Problem, find the second partials.(a) zxx (b) zyy (c) zxy (d) zyxz = ln (xy + 1)
In Problem, find the second partials.(a) zxx (b) zyy (c) zxy (d) zyxz = x2 ey2
In Problem, find each function’s relative maxima, relative minima, and saddle points, if they exist.z = 6xy - x3 - y2
In Problem, find the second partials.(a) zxx (b) zyy (c) zxy (d) zyxz = 3x3y4 - x2/y2
In Problem, find the second partials.(a) zxx (b) zyy (c) zxy (d) zyxz = x2y - 3xy
In Problem, find each function’s relative maxima, relative minima, and saddle points, if they exist.z = x3 + y3 - 6xy
Find the slope of the tangent in the x-direction to the surface z = 5x4 - 3xy2 + y2 at (1, 2, -3).
In Problem, find each function’s relative maxima, relative minima, and saddle points, if they exist.z = x2 + 5xy + 10y2 + 8x - 40y
In Problem, evaluate the functions at the given values of the independent variables.C(x1, x2) = 500 + 5x1 + 7x2; x1 = 200, x2 = 300
Find the partial derivative of f (x, y) = 4x3 - 5xy2 + y3 with respect to x at the point (1, 2, -8).
In Problem, find each function’s relative maxima, relative minima, and saddle points, if they exist.z = x2 + xy + y2 - 4y + 10x
In Problem, evaluate the functions at the given values of the independent variables.C(x1, x2) = 600 + 4x1 + 6x2; x1 = 400, x2 = 50
In Problem, find zx and zy.z = eln xy
In Problem, find each function’s relative maxima, relative minima, and saddle points, if they exist.z = 46 - x2 + 2xy - 4y2
In Problem, evaluate the functions at the given values of the independent variables.z = x2 + xy/x - y; x = 3, y = 2
In Problem, find each function’s relative maxima, relative minima, and saddle points, if they exist..z = 24 - x2 + xy - y2 + 36y
In Problem, find each function’s relative maxima, relative minima, and saddle points, if they exist.z = x2 - 4xy + y2 - 6y
Let f (x, y) = 2ex2y2. Find ∂2f/∂x ∂y.
Give the domain of each function in Problem.z = √x - y
Find ∂z/∂x if z = 5x3 + 6xy + y2.
Give the domain of each function in Problem.z = 4x3y - x/2x - y
If Q(K, L) = 70K2/3 L1/3, find Q(64,000, 512).
In Problem, find each function’s relative maxima, relative minima, and saddle points, if they exist.z = 3x2 + (y - 11)2 - 8
Suppose a company’s monthly production value Q in thousands of dollars is given by the Cobb-Douglas production functionQ = 10K0.45L0.55where K is thousands of dollars of capital investment per month and L is the total hours of labor per month. Capital investment is currently $10,000 per month,
If w(x, y, z) = x2 - 3yz, find w(2, 3, 1).
In Problem, find each function’s relative maxima, relative minima, and saddle points, if they exist.z = (x + 2)2 + y2 + 4
Let z = 6x2 1 x2y + y2 - 4y + 9. Find the pairs (x, y) that are critical points for z and then classify each as a relative maximum, a relative minimum, or a saddle point.
Find all first and second partial derivatives ofz = f (x, y) = 5x - 9y2 + 2(xy + 1)5
What is the domain of z = 3/2x - y?
Consider the function f (x, y) = 2x + 3y/√x2 - y.(a) Find the domain of f (x, y).(b) Evaluate f (-4, 12).
In a study of intelligence, the time (in seconds) for a laboratory animal to reach a reward in a maze was found to have probability density function f (t) = 10/t2 , t ≥ 10 where 10 seconds is the minimum time to traverse the maze. Find the probability that an animal chosen at random takes(a)
The length of time for students to complete a 1-hour timed standardized mathematics test has probability density function f (t) = 1.5t2 + t, 0 ≤ t ≤ 1 where t is the time in hours. Find the probability that the time it takes a randomly selected student to complete the test is(a) More than 45
The annual per capita share of U.S. total expenditures for heath care (in dollars per year) for selected years from 2002 and projected to2024 can be modeled byH(t) = 5330 e0.0442twhere t is the number of years after 2000. Assuming that the model remains valid, evaluate ∫2515 H(t) dt and tell what
The U.S. total annual health care costs (actual and projected, in billions of dollars) for selected years are given in the table. These costs can be modeled by C(t) = 0.32t3 - 7.7t2 + 170t + 1300 where C(t) is in billions of dollars per year and t is the number of years past 2000. Use a
In Problem, use properties of definite integrals.Evaluate (x +4x)6 dx.
The length of time (in years) until a copier feed mechanism needs to be replaced has probability density function given by f(t) = 0.6 e-0.6t t ≥ 0If one of these copiers is selected at random, find the probability that this mechanism lasts(a) more than 3 years.(b) more than 3 years given that it
A company uses wood chips in the manufacture of processed wood pieces of various sizes. Suppose the tons of wood chips T used per day has probability density functionf (T) = 0.125 e-0.125T(a) Find the probability of using more than 8 tons of wood chips in a day.(b) Find the number of tons T (to the
If the Lorenz curve for the income distribution for a given year has the form L(x) = xp and the Gini coefficient is G, find a formula for p.
Suppose the recorded Richter scale magnitude M of earthquakes in a certain region of South America has probability density function f (M) = 0.4 e-0.4MFind the probability that an earthquake in this region has magnitude greater than(a) 2.5.(b) 4.5.(c) 4.5 given it was greater than 2.5.
In a psychology experiment, laboratory rats are timed through a maze to reach a food reward. The minutes m required to reach the reward have probability density function f (m) = 1.5/m2 (m > 1.5).Find the probability that the time for a randomly selected lab rat to complete the maze is more
The Lorenz curves for the income distribution in the United States for all races for 2015 and for 1980 are given below. Find the Gini coefficient of income for both years and compare their distributions of income.2015: y = x2.661 1980: y = x2.241
A manufacturer of electrical components has determined that the length of time t (in hundreds of hours) before a certain one of its components fails has probability density functionf(t) = 2t e-t2Find the probability that a randomly selected one of these components lasts(a) More than 150 hours.(b)
Find the total income over the next 10 years from a continuous income stream that has an annual flow rate at time t given by f(t) = 125e0.05t in thousands of dollars per year.
The future value of $1000 invested in a savings account at 10% compounded continuously is S = 1000e0.1t, where t is in years. Find the average amount in the savings account during the first 5 years.
Suppose the probability density function for the life expectancy of a battery isFind the probability that a randomly selected battery lasts(a) 2 years or less.(b) At most half a year given that it lasts a year or less. S1.4e-14 -1.4x x2 0 f(x) = x
With data from the Social Security Trustees Report for selected years from 1950 and projected to 2030, the number of Social Security beneficiaries (in millions) can be modeled byB(t) = 0.00024t3 - 0.026t2 + 1.6t + 2.2where t is the number of years past 1950. Use the model to find the average number
The per capita disposable income (in dollars per year) in the United States for selected years from 2014 and projected to 2040 can be modeled byI(t) = 0.5532t2 + 738.5t + 34,430where t is the number of years past 2010. Use n = 10 equal subdivisions with right-hand endpoints to approximate (to the
Suppose that a definite integral is to be approximated and it is found that to achieve a specified accuracy, n must satisfy n ≥ 4.8. What is the smallest n that can be used, if (a) The Trapezoidal Rule is used?(b) Simpson’s Rule is used?
With U.S. Department of Energy data for selected years from 2000 and projected to 2030, sulphur dioxide emissions from electricity generation (in millions of short tons per year) can be modeled byE(x) = 0.0112x2 + 0.612x + 11.9where x is the number of years past 2000. Use n = 10 equal subdivisions
For which of the following functions f (x) doesgive the area between the graph of f (x) and the x-axis from x = 0 to x = 2?(a) f (x) = x2 + 1(b) f (x) = 2x2(c) f (x) = x - 1 |f(x) dx a. 0.
Evaluate the definite integrals in Problem. 4 (3x – 2)*x dx
In Problem, evaluate the improper integrals that converge. xe* dx 00
In the last half of the twentieth century, the U.S. population grew more diverse both racially and ethnically, with persons of Hispanic origin representing one of the fastest-growing segments. The table gives the percent of the U.S. civilian non-institutional population of Hispanic origin for
In Problem, find each function’s relative maxima, relative minima, and saddle points, if they exist.z = x2 + 6xy + y2 + 16x
Find x and y that maximize the utility function U = x3y subject to the budget constraint 30x + 20y = 8000.
Find the minimum value of z = 2x2 + y2 - xy subject to the constraint 2x + y = 8.
In Problem, find each function’s relative maxima, relative minima, and saddle points, if they exist.z = 4x2 + y2 + 4x + 1
Suppose a store sells two brands of disposable razors and the profit for these is a function of their two selling prices. The type 1 razor sells for $x, the type 2 sells for $y, and profit is given byP = 915x - 30x2 - 45xy + 975y - 30y2 - 3500Find the selling prices that maximize profit. Find the
Give the domain of each function in Problem.q = 5p1 2 - √p1 - p2
In Problem, find each function’s relative maxima, relative minima, and saddle points, if they exist.z = x2 + y2 - 2x + 4y + 5
Suppose the demand functions for two products areq1 = 300 - 2p1 - 5p2 and q2 = 150 - 4p1 - 7p2where q1 and q2 represent quantities demanded and p1 and p2 represent prices. What calculations enable us to decide whether the products are competitive or complementary? Are these products competitive or
Give the domain of each function in Problem.q = √p1 + 3p2
Find ∂z/∂y if z = 12x5 - 14x3y3 + 6y4 - 1.
In Problem, find each function’s relative maxima, relative minima, and saddle points, if they exist.z = 4y2 - x2 + 4y + 10x + 12
In Problem, find each function’s relative maxima, relative minima, and saddle points, if they exist.z = x2 - y2 + 4x - 6y + 11
The monthly payment R on a loan is a function of the amount borrowed, A, in thousands of dollars; the length of the loan, n, in years; and the annual interest rate, r, as a percent. Thus R = f (A, n, r). In parts (a) and (b), write a sentence that explains the practical meaning of each mathematical
In the figures, which of the shaded regions (A, B, C, or D) has the area given by(a)(b) f(x) dx?
The figure shows the sales growth rates under different levels of distribution and advertising from a to b. Set up an integral to determine the extra sales growth if $4 million is used in advertising rather than $2 million. $4 Million advertising $3 Million 8 advertising $2 Million h advertising a
Find c so that f(x) = c/x3 for x ≥ 5 is a probability density function.
A land developer is planning to dig a small lake and build a group of homes around it. To estimate the cost of the project, the area of the lake must be calculated from the proposed measurements (in feet) given in Figure and in the data in the table. Use Simpson’s Rule to approximate the area of
Crude oil and petroleum products are imported continuously by the United States. The following table and figure show the net expenditures forU.S. oil imports for selected years (in billions of dollars per year).(a) Use n = 5 equal subdivisions and left-hand endpoints to estimate the area under the
The annual per capita out-of-pocket expenses (to the nearest dollar) for U.S. health care for selected years from 2013 and projected to 2021 are shown in the table and figure.(a) Use n = 4 equal subdivisions and left-hand endpoints to estimate the area under the graph from 2013 to 2021.(b) What
Evaluate the integrals in Problem. Identify the formula used.∫e2x√3ex + 1 dx
Evaluate the definite integrals in Problem. 3x dx o 4x + 9
If the Lorenz curves for years a and b are given by La(x) and Lb(x), respectively, then from year a to year b, the change in the Gini coefficient (Gb - Ga) is given byIn Problem, complete the following.(a) Use the data in the table and make a new table for x and the corresponding values of [La(x) -
In Problem, find the average value of each function over the given interval.f (x) = 3√x over [-8, -1]
Evaluate the integrals in Problem. Identify the formula used.∫ dx/√4x2 + 7
Evaluate the definite integrals in Problem. 2 8x²e -* dx
If the Lorenz curves for years a and b are given by La(x) and Lb(x), respectively, then from year a to year b, the change in the Gini coefficient (Gb - Ga) is given byIn Problem, complete the following.(a) Use the data in the table and make a new table for x and the corresponding values of [La(x) -
If the supply function for x units of a commodity is p = 30 + 100 ln (2x + 1) dollars, what is the producer’s surplus at x = 30?
In Problem, use integration by parts to evaluate. re/2 6 In (2x) dx /0.5
Evaluate the integrals in Problem. Identify the formula used. e* 1 + e*
Evaluate the definite integrals in Problem.
In Problem, select the formula or method (I–IV) that should be used to evaluate each integral. Then evaluate the integral.I. Integration by partsII. ∫eu duIII. ∫ du/uIV. ∫un du x Vx – 1 dx
In Problem, use integration by parts to evaluate.∫ x dx/√x + 5

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