
Practical Business Math Procedures
12th Edition
ISBN: 9781259540554
Author: Jeffrey Slater, Sharon Wittry
Publisher: McGraw-Hill Education
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Chapter 1, Problem 44ECP
To determine
The value of the expression
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Q1.4
1 Point
V=C(R), the vector space of all real-valued continuous functions whose domain is the set R of
all real numbers, and H is the subset of C(R) consisting of all of the constant functions.
(e.g. the function ƒ : R → R defined by the formula f(x) = 3 for all x E R is an example of one
element of H.)
OH is a subspace of V.
H is not a subspace of V.
Save Answer
Solve the following LP problem using the Extreme Point Theorem:
Subject to:
Maximize Z-6+4y
2+y≤8
2x + y ≤10
2,y20
Solve it using the graphical method.
Guidelines for preparation for the teacher's
questions:
Understand the basics of Linear Programming (LP)
1. Know how to formulate an LP model.
2. Be able to identify decision variables, objective
functions, and constraints.
Be comfortable with graphical solutions
3. Know how to plot feasible regions and find extreme
points.
4. Understand how constraints affect the solution space.
Understand the Extreme Point Theorem
5. Know why solutions always occur at extreme points.
6. Be able to explain how optimization changes with
different constraints.
Think about real-world implications
7. Consider how removing or modifying constraints
affects the solution.
8. Be prepared to explain why LP problems are used in
business, economics, and operations research.
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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- Construct a table and find the indicated limit. √√x+2 If h(x) = then find lim h(x). X-8 X-8 Complete the table below. X 7.9 h(x) 7.99 7.999 8.001 8.01 8.1 (Type integers or decimals rounded to four decimal places as needed.)arrow_forwardExample 3.2. Solve the following boundary value problem by ADM (Adomian decomposition) method with the boundary conditions მი მი z- = 2x²+3 дг Əz w(x, 0) = x² - 3x, θω (x, 0) = i(2x+3). ayarrow_forwardUse the graph to find the following limits. (a) lim f(x) (b) lim f(x) X-1 x→1 (a) Find lim f(x) or state that it does not exist. Select the correct choice X-1 below and, if necessary, fill in the answer box within your choice. OA. lim f(x) = X-1 (Round to the nearest integer as needed.) OB. The limit does not exist. Qarrow_forward
- Officials in a certain region tend to raise the sales tax in years in which the state faces a budget deficit and then cut the tax when the state has a surplus. The graph shows the region's sales tax in recent years. Let T(x) represent the sales tax per dollar spent in year x. Find the desired limits and values, if they exist. Note that '01 represents 2001. Complete parts (a) through (e). Tax (in cents) T(X)4 8.5 8- OA. lim T(x)= cent(s) X-2007 (Type an integer or a decimal.) OB. The limit does not exist and is neither ∞ nor - ∞. Garrow_forwardDecide from the graph whether each limit exists. If a limit exists, estimate its value. (a) lim F(x) X➡-7 (b) lim F(x) X-2 (a) What is the value of the limit? Select the correct choice below and, if necessary, fill in the answer box within your choice. OA. lim F(x) = X-7 (Round to the nearest integer as needed.) OB. The limit does not exist. 17 Garrow_forwardFin lir X- a= (Us -10 OT Af(x) -10- 10arrow_forward
- Find all values x = a where the function is discontinuous. For each value of x, give the limit of the function as x approaches a. Be sure to note when the limit doesn't exist. f(x)=4x²+7x+1 Select the correct choice below and, if necessary, fill in the answer box(es) to complete your choice. (Use a comma to separate answers as needed.) OA. f is discontinuous at the single value x = B. f is discontinuous at the single value x = OC. f is discontinuous at the two values x = OD. fis discontinuous at the two values x = OE. f is discontinuous at the two values x = The limit is The limit does not exist and is not co or - oo. The limit for the smaller value is The limit for the larger value is The limit for both values do not exist and are not co or - co. The limit for the smaller value does not exist and is not oo or - co. The limit for the larger value isarrow_forwardFind all values x = a where the function is discontinuous. For each value of x, give the limit of the function as x approaches a. Be sure to note when the limit doesn't exist. 8+x f(x) = x(x-1) (Use a comma to separate answers as needed.) OA. The function f is discontinuous at the single value x = OB. The function f is discontinuous at the single value x = OC. The function f is discontinuous at the two values x = OD. The function f is discontinuous at the two values x = not oo or -0. OE. The function f is discontinuous at the two values x = The limit is The limit does not exist and is not oo or - co. The limits for both values do not exist and are not co or - co. The limit for the smaller value is The limit for the larger value does not exist and is The limit for the smaller value does not exist and is not co or - co. The limit for the largerarrow_forwardPls help ASAParrow_forward
- Q1 4 Points In each part, determine if the given set H is a subspace of the given vector space V. Q1.1 1 Point V = R and H is the set of all vectors in R4 which have the form a b x= 1-2a for some scalars a, b. 1+3b 2 (e.g., the vector x = is an example of one element of H.) OH is a subspace of V. OH is not a subspace of V. Save Answer Q1.2 1 Point V = P3, the vector space of all polynomials whose degree is at most 3, and H = +³, 3t2}. OH is a subspace of V. OH is not a subspace of V. Save Answer Span{2+ Q1.3 1 Point V = M2x2, the vector space of all 2 x 2 matrices, and H is the subset of M2x2 consisting of all invertible 2 × 2 matrices. OH is a subspace of V. OH is not a subspace of V. Save Answerarrow_forwardPls help ASAParrow_forwardPls help ASAParrow_forward
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