Practical Business Math Procedures
12th Edition
ISBN: 9781259540554
Author: Jeffrey Slater, Sharon Wittry
Publisher: McGraw-Hill Education
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Chapter 1, Problem 51ECP
(a)
To determine
The cost for a family of four leaving from Washington DC.
(b)
To determine
The cost for a family of four leaving from Los Angeles.
(c)
To determine
The extra cost needed for the family leaving from Los Angeles.
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use Lagrange multipliers to solve
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,…
Chapter 1 Solutions
Practical Business Math Procedures
Ch. 1.1 - Write in verbal form:
7,948
...Ch. 1.1 - Prob. 2PQCh. 1.1 - Kellogg’s reported its sales as five million, one...Ch. 1.1 - Write in verbal form:
8,682
...Ch. 1.1 - Prob. 2EPQCh. 1.1 - Kellogg’s reported its sales as three million, two...Ch. 1.1 - Express the following numbers in verbal...Ch. 1.1 - Write in numeric form:
Eighty thousand, two...Ch. 1.1 - Round the following numbers:
To the nearest...Ch. 1.1 - Round off each number to the nearest ten, nearest...
Ch. 1.1 - Name the place position (place value) of the...Ch. 1.1 - Gim Smith was shopping for an Apple computer. He...Ch. 1.1 - Amy Parker had to write a check at the bookstore...Ch. 1.1 - Matt Schaeffer was listening to the news and heard...Ch. 1.1 - Jackie Martin is the city clerk and must go to the...Ch. 1.1 - A government survey revealed that 25,963,400...Ch. 1.1 - Bob Donaldson wished to present his top student...Ch. 1.1 - Nancy Morrissey has a problem reading large...Ch. 1.2 - Add by totaling each separate column:
Ch. 1.2 - Estimate by rounding all the way (do not round the...Ch. 1.2 - Subtract and check your answer:
Ch. 1.2 - Jackson Manufacturing Company projected its year...Ch. 1.2 - Add by totaling each separate column:
Ch. 1.2 - Estimate by rounding all the way (do not round the...Ch. 1.2 - Subtract and check your answer:
Ch. 1.2 - Jackson Manufacturing Company projected its year...Ch. 1.2 - Add by totaling each separate column:
Ch. 1.2 - Prob. 2AHCh. 1.2 - Prob. 3AHCh. 1.2 - Subtract and check:
Ch. 1.2 - Prob. 5AHCh. 1.2 - Prob. 6AHCh. 1.2 - Prob. 7AHCh. 1.2 - Prob. 8AHCh. 1.2 - Prob. 9AHCh. 1.2 - Prob. 10AHCh. 1.2 - Prob. 11AHCh. 1.2 - Prob. 12AHCh. 1.2 - Prob. 13AHCh. 1.3 - Estimate the actual problem by rounding all the...Ch. 1.3 - Prob. 2PQCh. 1.3 - Prob. 3PQCh. 1.3 - Prob. 4PQCh. 1.3 - Prob. 5PQCh. 1.3 - Prob. 6PQCh. 1.3 - Prob. 1EPQCh. 1.3 - Prob. 2EPQCh. 1.3 - Prob. 3EPQCh. 1.3 - Prob. 4EPQCh. 1.3 - Prob. 5EPQCh. 1.3 - Prob. 6EPQCh. 1.3 - Prob. 1AHCh. 1.3 - Prob. 2AHCh. 1.3 - Prob. 3AHCh. 1.3 - Prob. 4AHCh. 1.3 - Prob. 5AHCh. 1.3 - Prob. 6AHCh. 1.3 - Prob. 7AHCh. 1.3 - Prob. 8AHCh. 1.3 - Prob. 9AHCh. 1.3 - Prob. 10AHCh. 1.3 - Prob. 11AHCh. 1.3 - Prob. 12AHCh. 1.3 - Ben Krenshaw’s supervisor at the construction site...Ch. 1 - Prob. 1ECPCh. 1 - Prob. 2ECPCh. 1 - Prob. 3ECPCh. 1 - Prob. 4ECPCh. 1 - Prob. 5ECPCh. 1 - Add the following: LU 1-2(1)
Ch. 1 - Prob. 7ECPCh. 1 - Prob. 8ECPCh. 1 - Prob. 9ECPCh. 1 - Prob. 10ECPCh. 1 - Prob. 11ECPCh. 1 - Prob. 12ECPCh. 1 - Prob. 13ECPCh. 1 - Multiply the following: LU 1-3(1)
Ch. 1 - Prob. 15ECPCh. 1 - Multiply the following: LU 1-3(1)
Ch. 1 - Multiply the following: LU 1-3(1)
Ch. 1 - Prob. 18ECPCh. 1 - Prob. 19ECPCh. 1 - Prob. 20ECPCh. 1 - Prob. 21ECPCh. 1 - Prob. 22ECPCh. 1 - Prob. 23ECPCh. 1 - Prob. 24ECPCh. 1 - Prob. 25ECPCh. 1 - Prob. 26ECPCh. 1 - Prob. 27ECPCh. 1 - Prob. 28ECPCh. 1 - Add the following and check by totaling each...Ch. 1 - Prob. 30ECPCh. 1 - Prob. 31ECPCh. 1 - Prob. 32ECPCh. 1 - Prob. 33ECPCh. 1 - Prob. 34ECPCh. 1 - Prob. 35ECPCh. 1 - Prob. 36ECPCh. 1 - Prob. 37ECPCh. 1 - Prob. 38ECPCh. 1 - Prob. 39ECPCh. 1 - Prob. 40ECPCh. 1 - Prob. 41ECPCh. 1 - Prob. 42ECPCh. 1 - Prob. 43ECPCh. 1 - Prob. 44ECPCh. 1 - Prob. 45ECPCh. 1 - Prob. 46ECPCh. 1 - Prob. 47ECPCh. 1 - Prob. 48ECPCh. 1 - Prob. 49ECPCh. 1 - Prob. 50ECPCh. 1 - Prob. 51ECPCh. 1 - Prob. 52ECPCh. 1 - Prob. 53ECPCh. 1 - Yahoo! Health reported in November 2014 that 6 out...Ch. 1 - Prob. 55ECPCh. 1 - Prob. 56ECPCh. 1 - Prob. 57ECPCh. 1 - Ron Alf, owner of Alf’s Moving Company, bought a...Ch. 1 - Prob. 59ECPCh. 1 - Prob. 60ECPCh. 1 - Prob. 61ECPCh. 1 - Prob. 62ECPCh. 1 - Prob. 63ECPCh. 1 - Prob. 64ECPCh. 1 - Prob. 65ECPCh. 1 - Prob. 66ECPCh. 1 - Roger Company produces beach balls and operates...Ch. 1 - Prob. 68ECPCh. 1 - Prob. 69ECPCh. 1 - Prob. 70ECPCh. 1 - Prob. 71ECPCh. 1 - Prob. 72ECPCh. 1 - Prob. 73ECPCh. 1 - Prob. 74ECPCh. 1 - Prob. 75ECPCh. 1 - Paula Sanchez is trying to determine her 2015...Ch. 1 - Prob. 1PTCh. 1 - Express the following number in verbal...Ch. 1 - Round the following numbers. LU 1-1(2)
Ch. 1 - Prob. 4PTCh. 1 - Prob. 5PTCh. 1 - Prob. 6PTCh. 1 - Prob. 7PTCh. 1 - Divide the following by the shortcut method. LU...Ch. 1 - Prob. 9PTCh. 1 - Sam Song plans to buy a $16,000 Ford Focus with an...Ch. 1 - Lester Hal has the oil tank at his business filled...
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