
Finite Mathematics and Calculus with Applications (10th Edition)
10th Edition
ISBN: 9780321979407
Author: Margaret L. Lial, Raymond N. Greenwell, Nathan P. Ritchey
Publisher: PEARSON
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Question
Chapter R.7, Problem 8E
To determine
To simplify: The expression
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Suppose a Cobb-Douglas Production function is given by the following:
P(L,K)=80L0.75 K-0.25
where L is units of labor, K is units of capital, and P(L, K) is total units that can be produced with this
labor/capital combination. Suppose each unit of labor costs $400 and each unit of capital costs $1,600.
Further suppose a total of $384,000 is available to be invested in labor and capital (combined).
A) How many units of labor and capital should be "purchased" to maximize production subject to your
budgetary constraint?
Units of labor, L =
Units of capital, K =
B) What is the maximum number of units of production under the given budgetary conditions? (Round your
answer to the nearest whole unit.)
Max production =
units
Suppose a Cobb-Douglas Production function is given by the function: P(L, K) = 7L0.0 K0.4
Furthemore, the cost function for a facility is given by the function: C(L, K) = 100L +400K
Suppose the monthly production goal of this facility is to produce 15,000 items. In this problem, we will
assume L represents units of labor invested and K represents units of capital invested, and that you can
invest in tenths of units for each of these. What allocation of labor and capital will minimize total
production Costs?
Units of Labor L =
Units of Capital K =
(Show your answer is exactly 1 decimal place)
(Show your answer is exactly 1 decimal place)
Also, what is the minimal cost to produce 15,000 units? (Use your rounded values for L and K from above
to answer this question.)
The minimal cost to produce 15,000 units is $
Hint:
1. Your constraint equation involves the Cobb Douglas Production function, not the Cost function.
2. When finding a relationship between L and K in your system of equations,…
Find the absolute maximum and minimum of f(x, y) = x + y within the domain x² + y² ≤ 4.
Please show your answers to at least 4 decimal places. Enter DNE if the value does not exist.
1. Absolute minimum of f(x, y) is
Chapter R Solutions
Finite Mathematics and Calculus with Applications (10th Edition)
Ch. R.1 - Perform the operation 3(x24x5)4(3x25x7)Ch. R.1 - Perform the operation (3y+2)(4y22y5).Ch. R.1 - Find (2x+7)(3x1) using the FOIL method.Ch. R.1 - Find (3x+2y)3.Ch. R.1 - Perform the indicated operations....Ch. R.1 - Perform the indicated operations....Ch. R.1 - Perform the indicated operations....Ch. R.1 - Perform the indicated operations....Ch. R.1 - Perform the indicated operations....Ch. R.1 - Perform the indicated operations....
Ch. R.1 - Perform the indicated operations. 7.9m(2m2+3m1)Ch. R.1 - Perform the indicated operations. 86x(2x3+5x+6)Ch. R.1 - Prob. 9ECh. R.1 - Perform the indicated operations. 10.(9k+q)(2kq)Ch. R.1 - Perform the indicated operations. 11.(23x)(2+3x)Ch. R.1 - Perform the indicated operations. 12.(6m+5)(6m5)Ch. R.1 - Perform the indicated operations....Ch. R.1 - Perform the indicated operations....Ch. R.1 - Perform the indicated operations....Ch. R.1 - Perform the indicated operations....Ch. R.1 - Perform the indicated operations....Ch. R.1 - Perform the indicated operations....Ch. R.1 - Perform the indicated operations....Ch. R.1 - Perform the indicated operations....Ch. R.1 - Perform the indicated operations....Ch. R.1 - Perform the indicated operations. 22.(x1)(x+2)(x3)Ch. R.1 - Perform the indicated operations. 23.(x+2)2Ch. R.1 - Perform the indicated operations. 24.(2a4b)2Ch. R.1 - Perform the indicated operations. 25.(x2y)3Ch. R.1 - Perform the indicated operations. 26.(3y+y)3Ch. R.2 - Factor 4z4+4z3+18z2.Ch. R.2 - Factor x23x10.Ch. R.2 - Factor 6a2+5ab4b2.Ch. R.2 - Factor each polynomial. If a polynomial cannot he...Ch. R.2 - Prob. 2ECh. R.2 - Prob. 3ECh. R.2 - Prob. 4ECh. R.2 - Prob. 5ECh. R.2 - Prob. 6ECh. R.2 - Prob. 7ECh. R.2 - Prob. 8ECh. R.2 - Prob. 9ECh. R.2 - Prob. 10ECh. R.2 - Prob. 11ECh. R.2 - Prob. 12ECh. R.2 - Prob. 13ECh. R.2 - Prob. 14ECh. R.2 - Prob. 15ECh. R.2 - Prob. 16ECh. R.2 - Factor each polynomial. If a polynomial cannot be...Ch. R.2 - Prob. 18ECh. R.2 - Factor each polynomial. If a polynomial cannot be...Ch. R.2 - Prob. 20ECh. R.2 - Factor each polynomial. If a polynomial cannot be...Ch. R.2 - Prob. 22ECh. R.2 - Prob. 23ECh. R.2 - Prob. 24ECh. R.2 - Prob. 25ECh. R.2 - Prob. 26ECh. R.2 - Prob. 27ECh. R.2 - Prob. 28ECh. R.2 - Factor each polynomial. If a polynomial cannot be...Ch. R.2 - Prob. 30ECh. R.2 - Prob. 31ECh. R.2 - Prob. 32ECh. R.3 - Write in lowest terms z2+5z+62z2+7z+3.Ch. R.3 - Prob. 2YTCh. R.3 - Write each rational expression in lowest terms....Ch. R.3 - Prob. 2ECh. R.3 - Write each rational expression in lowest terms....Ch. R.3 - Prob. 4ECh. R.3 - Write each rational expression in lowest terms....Ch. R.3 - Prob. 6ECh. R.3 - Write each rational expression in lowest terms....Ch. R.3 - Prob. 8ECh. R.3 - Write each rational expression in lowest terms....Ch. R.3 - Prob. 10ECh. R.3 - Write each rational expression in lowest terms....Ch. R.3 - Prob. 12ECh. R.3 - Prob. 13ECh. R.3 - Prob. 14ECh. R.3 - Prob. 15ECh. R.3 - Perform the indicated operations. 16.a316a332Ch. R.3 - Perform the indicated operations. 17.2k1664k323Ch. R.3 - Prob. 18ECh. R.3 - Prob. 19ECh. R.3 - Perform the indicated operations....Ch. R.3 - Prob. 21ECh. R.3 - Prob. 22ECh. R.3 - Prob. 23ECh. R.3 - Prob. 24ECh. R.3 - Prob. 25ECh. R.3 - Prob. 26ECh. R.3 - Prob. 27ECh. R.3 - Perform the indicated operations. 28.16m+25m+4mCh. R.3 - Prob. 29ECh. R.3 - Prob. 30ECh. R.3 - Prob. 31ECh. R.3 - Prob. 32ECh. R.3 - Prob. 33ECh. R.3 - Prob. 34ECh. R.3 - Prob. 35ECh. R.3 - Prob. 36ECh. R.3 - Prob. 37ECh. R.3 - Prob. 38ECh. R.4 - Solve 3x7=4(5x+2)7x.Ch. R.4 - Solve 2m2+7m=15.Ch. R.4 - Solve z2+6=8z.Ch. R.4 - Solve 1x24+2x2=1x.Ch. R.4 - Prob. 1ECh. R.4 - Prob. 2ECh. R.4 - Solve each equation. 3.0.2m0.5=0.1m+0.7Ch. R.4 - Prob. 4ECh. R.4 - Solve each equation. 5.3r+25(r+1)=6r+4Ch. R.4 - Solve each equation. 6.5(a+3)+4a5=(2a4)Ch. R.4 - Solve each equation. 7.2[3m2(3m)4]=6m4Ch. R.4 - Solve each equation. 8.4[2p(3p)+5]=7p2Ch. R.4 - Solve each equation by factoring or by using the...Ch. R.4 - Prob. 10ECh. R.4 - Solve each equation by factoring or by using the...Ch. R.4 - Solve each equation by factoring or by using the...Ch. R.4 - Solve each equation by factoring or by using the...Ch. R.4 - Solve each equation by factoring or by using the...Ch. R.4 - Solve each equation by factoring or by using the...Ch. R.4 - Solve each equation by factoring or by using the...Ch. R.4 - Solve each equation by factoring or by using the...Ch. R.4 - Solve each equation by factoring or by using the...Ch. R.4 - Solve each equation by factoring or by using the...Ch. R.4 - Solve each equation by factoring or by using the...Ch. R.4 - Prob. 21ECh. R.4 - Prob. 22ECh. R.4 - Solve each equation by factoring or by using the...Ch. R.4 - Solve each equation by factoring or by using the...Ch. R.4 - Solve each equation by factoring or by using the...Ch. R.4 - Solve each equation by factoring or by using the...Ch. R.4 - Prob. 27ECh. R.4 - Prob. 28ECh. R.4 - Solve each equation. 29.4x382x+5+3x3=0Ch. R.4 - Solve each equation. 30.5p27p+2=12p24Ch. R.4 - Solve each equation. 31.2mm26m=12m22mCh. R.4 - Solve each equation. 32.2yy1=5y+108yy2yCh. R.4 - Solve each equation. 33.1x23xx1=2x+1x23x+2Ch. R.4 - Solve each equation. 34.5a+7a+1=a22a+4a2+aCh. R.4 - Solve each equation. 35.5b+54b2+2b=6b2+7b+10Ch. R.4 - Solve each equation. 36.2x22x3+5x2x6=1x2+3x+2Ch. R.4 - Prob. 37ECh. R.5 - Prob. 1YTCh. R.5 - Prob. 2YTCh. R.5 - Prob. 3YTCh. R.5 - Prob. 1ECh. R.5 - Prob. 2ECh. R.5 - Write each expression in interval notation, Graph...Ch. R.5 - Write each expression in interval notation, Graph...Ch. R.5 - Prob. 5ECh. R.5 - Prob. 6ECh. R.5 - Using the variable x, write each interval as an...Ch. R.5 - Prob. 8ECh. R.5 - Using the variable x, write each interval as an...Ch. R.5 - Prob. 10ECh. R.5 - Prob. 11ECh. R.5 - Prob. 12ECh. R.5 - Using the variable x, write each interval as an...Ch. R.5 - Prob. 14ECh. R.5 - Prob. 15ECh. R.5 - Prob. 16ECh. R.5 - Prob. 17ECh. R.5 - Prob. 18ECh. R.5 - Solve each inequality and graph the solution....Ch. R.5 - Prob. 20ECh. R.5 - Prob. 21ECh. R.5 - Prob. 22ECh. R.5 - Solve each inequality and graph the solution....Ch. R.5 - Prob. 24ECh. R.5 - Prob. 25ECh. R.5 - Prob. 26ECh. R.5 - Prob. 27ECh. R.5 - Prob. 28ECh. R.5 - Prob. 29ECh. R.5 - Prob. 30ECh. R.5 - Solve each inequality. Graph each solution....Ch. R.5 - Prob. 32ECh. R.5 - Prob. 33ECh. R.5 - Prob. 34ECh. R.5 - Prob. 35ECh. R.5 - Prob. 36ECh. R.5 - Prob. 37ECh. R.5 - Prob. 38ECh. R.5 - Prob. 39ECh. R.5 - Prob. 40ECh. R.5 - Prob. 41ECh. R.5 - Prob. 42ECh. R.5 - Prob. 43ECh. R.5 - Prob. 44ECh. R.5 - Solve each inequality. 45.k1k+21Ch. R.5 - Prob. 46ECh. R.5 - Prob. 47ECh. R.5 - Prob. 48ECh. R.5 - Prob. 49ECh. R.5 - Prob. 50ECh. R.5 - Prob. 51ECh. R.5 - Prob. 52ECh. R.5 - Prob. 53ECh. R.5 - Prob. 54ECh. R.6 - Prob. 1YTCh. R.6 - Prob. 2YTCh. R.6 - Prob. 3YTCh. R.6 - Prob. 4YTCh. R.6 - Prob. 5YTCh. R.6 - Prob. 6YTCh. R.6 - Prob. 1ECh. R.6 - Prob. 2ECh. R.6 - Prob. 3ECh. R.6 - Prob. 4ECh. R.6 - Prob. 5ECh. R.6 - Prob. 6ECh. R.6 - Prob. 7ECh. R.6 - Prob. 8ECh. R.6 - Prob. 9ECh. R.6 - Prob. 10ECh. R.6 - Prob. 11ECh. R.6 - Prob. 12ECh. R.6 - Prob. 13ECh. R.6 - Prob. 14ECh. R.6 - Prob. 15ECh. R.6 - Prob. 16ECh. R.6 - Prob. 17ECh. R.6 - Prob. 18ECh. R.6 - Prob. 19ECh. R.6 - Prob. 20ECh. R.6 - Prob. 21ECh. R.6 - Prob. 22ECh. R.6 - Prob. 23ECh. R.6 - Prob. 24ECh. R.6 - Prob. 25ECh. R.6 - Prob. 26ECh. R.6 - Write each number without exponents. 27.1211/2Ch. R.6 - Prob. 28ECh. R.6 - Prob. 29ECh. R.6 - Prob. 30ECh. R.6 - Prob. 31ECh. R.6 - Prob. 32ECh. R.6 - Prob. 33ECh. R.6 - Prob. 34ECh. R.6 - Prob. 35ECh. R.6 - Prob. 36ECh. R.6 - Prob. 37ECh. R.6 - Prob. 38ECh. R.6 - Prob. 39ECh. R.6 - Prob. 40ECh. R.6 - Prob. 41ECh. R.6 - Prob. 42ECh. R.6 - Prob. 43ECh. R.6 - Prob. 44ECh. R.6 - Prob. 45ECh. R.6 - Prob. 46ECh. R.6 - Prob. 47ECh. R.6 - Simplify each expression. Write all answers with...Ch. R.6 - Prob. 49ECh. R.6 - Prob. 50ECh. R.6 - Prob. 51ECh. R.6 - Prob. 52ECh. R.6 - Prob. 53ECh. R.6 - Prob. 54ECh. R.6 - Prob. 55ECh. R.6 - Prob. 56ECh. R.7 - Simplify 28x9y5.Ch. R.7 - Rationalize the denominator in 5xy.Ch. R.7 - Rationalize the numerator in 4+x16x.Ch. R.7 - Simplify each expression by removing as many...Ch. R.7 - Simplify each expression by removing as many...Ch. R.7 - Simplify each expression by removing as many...Ch. R.7 - Prob. 4ECh. R.7 - Simplify each expression by removing as many...Ch. R.7 - Simplify each expression by removing as many...Ch. R.7 - Prob. 7ECh. R.7 - Prob. 8ECh. R.7 - Simplify each expression by removing as many...Ch. R.7 - Simplify each expression by removing as many...Ch. R.7 - Simplify each expression by removing as many...Ch. R.7 - Simplify each expression by removing as many...Ch. R.7 - Simplify each expression by removing as many...Ch. R.7 - Simplify each expression by removing as many...Ch. R.7 - Simplify each expression by removing as many...Ch. R.7 - Prob. 16ECh. R.7 - Simplify each expression by removing as many...Ch. R.7 - Prob. 18ECh. R.7 - Simplify each expression by removing as many...Ch. R.7 - Prob. 20ECh. R.7 - Simplify each expression by removing as many...Ch. R.7 - Prob. 22ECh. R.7 - Prob. 23ECh. R.7 - Prob. 24ECh. R.7 - Prob. 25ECh. R.7 - Simplify each root, if possible. 26.9k2+h2Ch. R.7 - Rationalize each denominator. Assume that all...Ch. R.7 - Prob. 28ECh. R.7 - Rationalize each denominator. Assume that all...Ch. R.7 - Prob. 30ECh. R.7 - Rationalize each denominator. Assume that all...Ch. R.7 - Prob. 32ECh. R.7 - Rationalize each denominator. Assume that all...Ch. R.7 - Prob. 34ECh. R.7 - Rationalize each denominator. Assume that all...Ch. R.7 - Prob. 36ECh. R.7 - Prob. 37ECh. R.7 - Prob. 38ECh. R.7 - Rationalize each denominator. Assume that all...Ch. R.7 - Rationalize each denominator. Assume that all...Ch. R.7 - Rationalize each denominator. Assume that all...Ch. R.7 - Prob. 42ECh. R.7 - Prob. 43ECh. R.7 - Rationalize each denominator. Assume that all...
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