Finite Mathematics for the Managerial, Life, and Social Sciences
12th Edition
ISBN: 9781337405782
Author: Soo T. Tan
Publisher: Cengage Learning
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Chapter 5.4, Problem 6E
To determine
To find:
The first five terms of the arithmetic progression.
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Students have asked these similar questions
You manage a chemical company with 2 warehouses. The following quantities of
Important Chemical A have arrived from an international supplier at 3 different
ports:
Chemical Available (L)
Port 1
Port 2
Port 3
400
110
100
The following amounts of Important Chemical A are required at your warehouses:
Warehouse 1
Warehouse 2
Chemical Required (L)
380
230
The cost in £ to ship 1L of chemical from each port to each warehouse is as follows:
Warehouse 1 Warehouse 2
Port 1
£10
£45
Port 2
£20
£28
Port 3
£13
£11
(a) You want to know how to send these shipments as cheaply as possible. For-
mulate this as a linear program (you do not need to formulate it in standard
inequality form) indicating what each variable represents.
a) Suppose that we are carrying out the 1-phase simplex algorithm on a linear program in
standard inequality form (with 3 variables and 4 constraints) and suppose that we have
reached a point where we have obtained the following tableau. Apply one more pivot
operation, indicating the highlighted row and column and the row operations you carry
out. What can you conclude from your updated tableau?
x1 12 23
81
82
83
S4
$1
-20
1 1
0
0
0
3
82
3 0
-2
0
1
2
0
6
12
1
1
-3
0
0
1
0
2
84
-3 0
2
0
0
-1 1 4
2
-2
0 11
0
0
-4
0
-8
b) Solve the following linear program using the 2-phase simplex algorithm. You should give
the initial tableau and each further tableau produced during the execution of the
algorithm. If the program has an optimal solution, give this solution and state its
objective value. If it does not have an optimal solution, say why.
maximize 21 - - 2x2 + x3 - 4x4
subject to 2x1+x22x3x4≥ 1,
5x1+x2-x3-4 -1,
2x1+x2-x3-342,
1, 2, 3, 4 ≥0.
Suppose we have a linear program in standard equation form
maximize c'x
subject to Ax=b,
x≥ 0.
and suppose u, v, and w are all optimal solutions to this linear program.
(a) Prove that zu+v+w is an optimal solution.
(b) If you try to adapt your proof from part (a) to prove that that u+v+w
is an optimal solution, say exactly which part(s) of the proof go wrong.
(c) If you try to adapt your proof from part (a) to prove that u+v-w is an
optimal solution, say exactly which part(s) of the proof go wrong.
Chapter 5 Solutions
Finite Mathematics for the Managerial, Life, and Social Sciences
Ch. 5.1 - Explain the difference between simple interest and...Ch. 5.1 - Prob. 2CQCh. 5.1 - Prob. 3CQCh. 5.1 - Find the simple interest on a 500 investment made...Ch. 5.1 - Prob. 2ECh. 5.1 - Find the accumulated amount at the end of 9months...Ch. 5.1 - Find the accumulated amount at the end of 8months...Ch. 5.1 - Prob. 5ECh. 5.1 - A bank deposit paying simple interest at the rate...Ch. 5.1 - How many days will it take for 1000 to earn 20...
Ch. 5.1 - How many days will it take for 1500 to earn 25...Ch. 5.1 - A bank deposit paying simple interest grew from an...Ch. 5.1 - Determine the simple interest rate at which 1200...Ch. 5.1 - Prob. 11ECh. 5.1 - Prob. 12ECh. 5.1 - Prob. 13ECh. 5.1 - Prob. 14ECh. 5.1 - Prob. 15ECh. 5.1 - Prob. 16ECh. 5.1 - Prob. 17ECh. 5.1 - Prob. 18ECh. 5.1 - Prob. 19ECh. 5.1 - Prob. 20ECh. 5.1 - In Exercises 21-24, find the effective rate...Ch. 5.1 - Prob. 22ECh. 5.1 - In Exercises 21-24, find the effective rate...Ch. 5.1 - In Exercises 21-24, find the effective rate...Ch. 5.1 - In Exercises 25-28, find the present value of...Ch. 5.1 - Prob. 26ECh. 5.1 - Prob. 27ECh. 5.1 - Prob. 28ECh. 5.1 - Find the accumulated amount after 4years if 5000...Ch. 5.1 - Prob. 30ECh. 5.1 - Prob. 31ECh. 5.1 - Prob. 32ECh. 5.1 - CONSUMER DECISIONS Mitchell has been given the...Ch. 5.1 - COURT JUDGMENT Jennifer was awarded damages of...Ch. 5.1 - BRIDGE LOANS To help finance the purchase of a new...Ch. 5.1 - CORPORATE BONDS David owns 20,000 worth of 10-year...Ch. 5.1 - MUNICIPAL BONDS Maya paid 10,000 for a 7-year bond...Ch. 5.1 - TREASURY BILLS Isabella purchased 20,000 worth of...Ch. 5.1 - TREASURY BILLS Maxwell purchased 15,000 worth of...Ch. 5.1 - COMPARING INVESTMENT RETURNS The value of Marias...Ch. 5.1 - Prob. 41ECh. 5.1 - INVESTMENTS The value of Jacks investment...Ch. 5.1 - INVESTMENTS The value of Arabellas stock portfolio...Ch. 5.1 - Write Formula 1b in the slope intercept form, and...Ch. 5.1 - HOSPITAL COSTS If the cost of a semiprivate room...Ch. 5.1 - FAMILY FOOD EXPENDITURE Today, a typical family of...Ch. 5.1 - HOUSING APPRECIATION The Kwans are planning to buy...Ch. 5.1 - Prob. 48ECh. 5.1 - PENSION FUNDS The managers of a pension fund have...Ch. 5.1 - RETIREMENT FUNDS Five and a half years ago, Chris...Ch. 5.1 - MUTUAL FUNDS Jodie invested 15,000 in a mutual...Ch. 5.1 - TRUST FUNDS A young man is the beneficiary of a...Ch. 5.1 - Prob. 53ECh. 5.1 - PROMISSORY NOTES An individual purchased a 4-year,...Ch. 5.1 - INVESTMENT PLANNING Find how much money should be...Ch. 5.1 - Prob. 56ECh. 5.1 - COMPARING RATES OF RETURN In the last 5 years,...Ch. 5.1 - COMPARING RATES OF RETURN Fleet Street Savings...Ch. 5.1 - Prob. 59ECh. 5.1 - Prob. 60ECh. 5.1 - LOAN CONSOLIDATION The proprietors of The Coachmen...Ch. 5.1 - Prob. 62ECh. 5.1 - ZERO COUPON BONDS Juan is contemplating buying a...Ch. 5.1 - REVENUE GROWTH OF A HOME THEATER BUSINESS Maxwell...Ch. 5.1 - Prob. 65ECh. 5.1 - PURCHASING POWER The inflation rates in the U.S....Ch. 5.1 - Prob. 67ECh. 5.1 - Prob. 68ECh. 5.1 - SAVING FOR COLLEGE Having received a large...Ch. 5.1 - Prob. 70ECh. 5.1 - REAL ESTATE INVESTMENT An investor purchased a...Ch. 5.1 - Prob. 72ECh. 5.1 - Prob. 73ECh. 5.1 - Use the formula given in Exercise 73 to solve...Ch. 5.1 - Use the formula given in Exercise 73 to solve...Ch. 5.1 - COMMON STOCK TRANSACTION Steven purchased 1000...Ch. 5.1 - ZERO COUPON BONDS Nina purchased a zero coupon...Ch. 5.1 - Prob. 78ECh. 5.1 - Prob. 79ECh. 5.1 - Prob. 80ECh. 5.1 - Prob. 81ECh. 5.1 - Prob. 82ECh. 5.1 - optional In exercise 8390, use logarithms to solve...Ch. 5.1 - Prob. 84ECh. 5.1 - optional In exercise 8390, use logarithms to solve...Ch. 5.1 - Optional In Exercises 8390, use logarithms to...Ch. 5.1 - Optional In Exercise 8390, use logarithms to solve...Ch. 5.1 - Prob. 88ECh. 5.1 - Optional In Exercises 8390, use logarithms to...Ch. 5.1 - RULE OF 70The rule of 70 is a rule of thumb for...Ch. 5.1 - Prob. 1TECh. 5.1 - Prob. 2TECh. 5.1 - Prob. 3TECh. 5.1 - Prob. 4TECh. 5.1 - Prob. 5TECh. 5.1 - Prob. 6TECh. 5.1 - Prob. 7TECh. 5.1 - Prob. 8TECh. 5.1 - Prob. 9TECh. 5.1 - Prob. 10TECh. 5.1 - Prob. 11TECh. 5.1 - Prob. 12TECh. 5.2 - Is the term of an ordinary annuity fixed or...Ch. 5.2 - Prob. 2CQCh. 5.2 - Prob. 3CQCh. 5.2 - Prob. 4CQCh. 5.2 - In Exercises 1-8, find the amount future value of...Ch. 5.2 - Prob. 2ECh. 5.2 - In Exercises 1-8, find the amount future value of...Ch. 5.2 - Prob. 4ECh. 5.2 - In Exercises 1-8, find the amount future value of...Ch. 5.2 - Prob. 6ECh. 5.2 - In Exercises 1-8, find the amount future value of...Ch. 5.2 - In Exercises 1-8, find the amount future value of...Ch. 5.2 - Prob. 9ECh. 5.2 - Prob. 10ECh. 5.2 - In Exercises 9-14, find the present value of each...Ch. 5.2 - Prob. 12ECh. 5.2 - In Exercises 9-14, find the present value of each...Ch. 5.2 - Prob. 14ECh. 5.2 - IRAs If a merchant deposits 1500 at the end of...Ch. 5.2 - SAVINGS ACCOUNTS If Jackson deposits 100 at the...Ch. 5.2 - SAVINGS ACCOUNTS Linda has joined a Christmas Fund...Ch. 5.2 - KEOGH ACCOUNTS Robin, who is self-employed,...Ch. 5.2 - INVESTMENT ANALYSIS Karen has been depositing 150...Ch. 5.2 - RETIREMENT PLANNING As a fringe benefit for the...Ch. 5.2 - INVESTMENT ANALYSIS Luis has 150,000 in his...Ch. 5.2 - AUTO LEASING The Betzes have leased an auto for 2...Ch. 5.2 - SAVINGS ACCOUNTS The Pirerras are planning to go...Ch. 5.2 - INSTALLMENT PLANS Mikes Sporting Goods sells...Ch. 5.2 - AUTO FINANCING Lupe made a down payment of 8000...Ch. 5.2 - LOTTERY PAYOUTS A state lottery commission pays...Ch. 5.2 - PURCHASING A HOME The Johnsons have accumulated a...Ch. 5.2 - PURCHASING A HOME Refer to Exercise 27. If local...Ch. 5.2 - Prob. 29ECh. 5.2 - SAVINGS PLAN Lauren plans to deposit 5000 into a...Ch. 5.2 - FINANCIAL PLANNING Joe plans to deposit 200 at the...Ch. 5.2 - INVESTMENT ANALYSIS From age 25 to age 40, Jessica...Ch. 5.2 - ROTH IRAS Suppose that Jacob deposits 3000/year...Ch. 5.2 - RETIREMENT PLANNING Suppose that Ramos contributes...Ch. 5.2 - Prob. 35ECh. 5.2 - Prob. 36ECh. 5.2 - Prob. 1TECh. 5.2 - Prob. 2TECh. 5.2 - Prob. 3TECh. 5.2 - Prob. 4TECh. 5.2 - Prob. 5TECh. 5.2 - Prob. 6TECh. 5.2 - Prob. 7TECh. 5.2 - Prob. 8TECh. 5.3 - Write the amortization formula. a. If P and i are...Ch. 5.3 - Prob. 2CQCh. 5.3 - In Exercises 1-8, find the periodic payment R...Ch. 5.3 - Prob. 2ECh. 5.3 - In Exercises 1-8, find the periodic payment R...Ch. 5.3 - Prob. 4ECh. 5.3 - In Exercises 1-8, find the periodic payment R...Ch. 5.3 - Prob. 6ECh. 5.3 - In Exercises 1-8, find the periodic payment R...Ch. 5.3 - Prob. 8ECh. 5.3 - In Exercises 9-14, find the periodic payment R...Ch. 5.3 - Prob. 10ECh. 5.3 - In Exercises 9-14, find the periodic payment R...Ch. 5.3 - Prob. 12ECh. 5.3 - In Exercises 9-14, find the periodic payment R...Ch. 5.3 - Prob. 14ECh. 5.3 - Prob. 15ECh. 5.3 - Suppose payments were made at the end of each...Ch. 5.3 - Suppose payments will be made for 612 years at the...Ch. 5.3 - Suppose payments will be made for 914 years at the...Ch. 5.3 - LOAN AMORTIZATION A sum of 100,000 is to be repaid...Ch. 5.3 - Prob. 20ECh. 5.3 - HOME MORTAGES Complete the following table which...Ch. 5.3 - FINANCING A HOME The Flemings secured a bank loan...Ch. 5.3 - FINANCING A CAR The price of a new car is 20,000....Ch. 5.3 - Prob. 24ECh. 5.3 - FINANCIAL ANALYSIS A group of private investors...Ch. 5.3 - Prob. 26ECh. 5.3 - FINANCING A HOME The Taylors have purchased a...Ch. 5.3 - FINANCIAL PLANNING Jessica wants to accumulate...Ch. 5.3 - SINKING FUNDS A city has 2.5 million worth of...Ch. 5.3 - TRUST FUNDS Carl is the beneficiary of a 20,000...Ch. 5.3 - SINKING FUNDS Lowell Corporation wishes to...Ch. 5.3 - SINKING FUNDS The management of Gibraltar...Ch. 5.3 - RETIREMENT ACCOUNTS Andrea, a self-employed...Ch. 5.3 - STUDENT LOANS Joe Secure a loan of 12000 3years...Ch. 5.3 - RETIREMENT ACCOUNTS Robin wishes to accumulate...Ch. 5.3 - FINANCING COLLEGE EXPENSES Yumis grandparents...Ch. 5.3 - IRAs Martin has deposited 375 in his IRA at the...Ch. 5.3 - RETIREMENT PLANNING Jennifer is the owner of a...Ch. 5.3 - Prob. 39ECh. 5.3 - FINANCING A CAR Darla purchased a new car during a...Ch. 5.3 - AUTO FINANCING Dan is contemplating trading in his...Ch. 5.3 - AUTO FINANCING Paula is considering the purchase...Ch. 5.3 - FINANCING A HOME Eight years ago, Kim secured a...Ch. 5.3 - FINANCING A HOME Sarah secured a bank loan of...Ch. 5.3 - PERSONAL LOANS Two years ago, Paul borrowed 10,000...Ch. 5.3 - INVESTMENT ANALYSIS Since he was 22 years old, Ben...Ch. 5.3 - BALLOON PAYMENT MORTGAGES Emilio is securing a...Ch. 5.3 - BALLOON PAYMENT MORTGAGES Olivia plans to secure a...Ch. 5.3 - HOME REFINANCING Four years ago, Emily secured a...Ch. 5.3 - HOME REFINANCING Five years ago, Diane secured a...Ch. 5.3 - REFINANCING A HOME The Sandersons are planning to...Ch. 5.3 - REFINANCING A HOME Josh purchased a condominium 5...Ch. 5.3 - Prob. 53ECh. 5.3 - ADJUSTABLE-RATE MORTGAGES George secured an...Ch. 5.3 - Prob. 55ECh. 5.3 - REFINANCING A HOME: The Martinezes are planning to...Ch. 5.3 - Prob. 57ECh. 5.3 - Prob. 58ECh. 5.3 - HOME AFFORDABILITY: Suppose that the Carlsons have...Ch. 5.3 - Prob. 60ECh. 5.3 - Prob. 1TECh. 5.3 - Prob. 2TECh. 5.3 - Prob. 3TECh. 5.3 - Prob. 4TECh. 5.3 - Prob. 5TECh. 5.3 - Prob. 6TECh. 5.3 - Prob. 7TECh. 5.3 - Prob. 8TECh. 5.3 - Prob. 9TECh. 5.3 - Prob. 10TECh. 5.4 - Suppose an arithmetic progression has first term a...Ch. 5.4 - Prob. 2CQCh. 5.4 - Prob. 1ECh. 5.4 - Prob. 2ECh. 5.4 - Prob. 3ECh. 5.4 - Prob. 4ECh. 5.4 - Prob. 5ECh. 5.4 - Prob. 6ECh. 5.4 - Prob. 7ECh. 5.4 - Prob. 8ECh. 5.4 - Find the sum of first 15 terms of the arithmetic...Ch. 5.4 - Prob. 10ECh. 5.4 - Find the sum of odd integers between 14 and 58.Ch. 5.4 - Prob. 12ECh. 5.4 - Prob. 13ECh. 5.4 - Prob. 14ECh. 5.4 - Prob. 15ECh. 5.4 - SALES GROWTH Moderne Furniture Company had sales...Ch. 5.4 - EXERCISE PROGRAM As part of her fitness program,...Ch. 5.4 - COST OF DRILLING A 100-ft oil well is to be...Ch. 5.4 - Prob. 19ECh. 5.4 - Prob. 20ECh. 5.4 - SUM-OF-THE-YEARS-DIGITS METHOD OF DEPRECIATION One...Ch. 5.4 - SUM-OF-THE-YEARS-DIGITS METHOD OF DEPRECIATION The...Ch. 5.4 - In Exercises 23-28, determine which of the...Ch. 5.4 - In Exercises 23-28, determine which of the...Ch. 5.4 - Prob. 25ECh. 5.4 - In Exercises 23-28, determine which of the...Ch. 5.4 - In Exercises 23-28, determine which of the...Ch. 5.4 - Prob. 28ECh. 5.4 - Prob. 29ECh. 5.4 - Prob. 30ECh. 5.4 - Prob. 31ECh. 5.4 - Prob. 32ECh. 5.4 - Prob. 33ECh. 5.4 - Prob. 34ECh. 5.4 - Prob. 35ECh. 5.4 - Prob. 36ECh. 5.4 - Prob. 37ECh. 5.4 - Prob. 38ECh. 5.4 - Prob. 39ECh. 5.4 - Prob. 40ECh. 5.4 - Prob. 41ECh. 5.4 - DOUBLE DECLINING-BALANCE METHOD OF DEPRECIATION...Ch. 5.4 - Prob. 43ECh. 5.4 - Prob. 44ECh. 5.CRQ - Fill in the blanks. a. Simple interest is computed...Ch. 5.CRQ - Prob. 2CRQCh. 5.CRQ - Prob. 3CRQCh. 5.CRQ - Prob. 4CRQCh. 5.CRQ - Prob. 5CRQCh. 5.CRQ - Prob. 6CRQCh. 5.CRQ - Prob. 7CRQCh. 5.CRQ - Prob. 8CRQCh. 5.CRE - Prob. 1CRECh. 5.CRE - Prob. 2CRECh. 5.CRE - Find the effective rate of interest corresponding...Ch. 5.CRE - Prob. 4CRECh. 5.CRE - Prob. 5CRECh. 5.CRE - Prob. 6CRECh. 5.CRE - Prob. 7CRECh. 5.CRE - Prob. 8CRECh. 5.CRE - Prob. 9CRECh. 5.CRE - Prob. 10CRECh. 5.CRE - Prob. 11CRECh. 5.CRE - Prob. 12CRECh. 5.CRE - Prob. 13CRECh. 5.CRE - Prob. 14CRECh. 5.CRE - Prob. 15CRECh. 5.CRE - Prob. 16CRECh. 5.CRE - Prob. 17CRECh. 5.CRE - Prob. 18CRECh. 5.CRE - Prob. 19CRECh. 5.CRE - Prob. 20CRECh. 5.CRE - INVESTMENTS Anthony invested a sum of money 5...Ch. 5.CRE - Prob. 22CRECh. 5.CRE - Prob. 23CRECh. 5.CRE - MUTUAL FUNDS Juan invested 24.000 in a mutual fund...Ch. 5.CRE - COLLEGE SAVINGS PROGRAM The Blakes have decided to...Ch. 5.CRE - RETIREMENT ACCOUNTS Mai Lee has contributed 200 at...Ch. 5.CRE - Prob. 27CRECh. 5.CRE - INSTALLMENT FINANCING Peggy made a down payment of...Ch. 5.CRE - HOME FINANCING The Turners have purchased a house...Ch. 5.CRE - Prob. 30CRECh. 5.CRE - Prob. 31CRECh. 5.CRE - SINKING FUNDS The management of a condominium...Ch. 5.CRE - CREDIT CARD PAYMENTS The outstanding balance on...Ch. 5.CRE - Prob. 34CRECh. 5.BMO - Find the accumulated amount at the end of 3 years...Ch. 5.BMO - Prob. 2BMOCh. 5.BMO - Prob. 3BMOCh. 5.BMO - Prob. 4BMOCh. 5.BMO - Prob. 5BMOCh. 5.BMO - a. Find the sum of the first ten terms of the...
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