Finite Mathematics, Books a la Carte Plus MyLab Math Access Card Package (11th Edition)
11th Edition
ISBN: 9780133886818
Author: Margaret L. Lial, Raymond N. Greenwell, Nathan P. Ritchey
Publisher: PEARSON
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Chapter 5, Problem 3RE
To determine
If the provided statement is true or false
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The Martin-Beck Company operates a plant in St. Louis with an annual capacity of 30,000 units. Product is shipped to regional distribution centers located in Boston, Atlanta, and Houston. Because of an anticipated increase in demand, Martin-Beck plans to increase capacity by constructing a new plant in one or more of the following cities: Detroit, Toledo, Denver, or Kansas. The following is a linear program used to
determine which cities Martin-Beck should construct a plant in.
Let
y₁ = 1 if a plant is constructed in Detroit; 0 if not
y₂ = 1 if a plant is constructed in Toledo; 0 if not
y₂ = 1 if a plant is constructed in Denver; 0 if not
y = 1 if a plant is constructed in Kansas City; 0 if not.
The variables representing the amount shipped from each plant site to each distribution center are defined just as for a transportation problem.
*,, = the units shipped in thousands from plant i to distribution center j
i = 1 (Detroit), 2 (Toledo), 3 (Denver), 4 (Kansas City), 5 (St.Louis) and…
Consider the following mixed-integer linear program.
Max
3x1
+
4x2
s.t.
4x1
+
7x2
≤
28
8x1
+
5x2
≤
40
x1, x2 ≥ and x1 integer
(a)
Graph the constraints for this problem. Indicate on your graph all feasible mixed-integer solutions.
On the coordinate plane the horizontal axis is labeled x1 and the vertical axis is labeled x2. A region bounded by a series of connected line segments, and several horizontal lines are on the graph.
The series of line segments connect the approximate points (0, 4), (3.889, 1.778), and (5, 0).
The region is above the horizontal axis, to the right of the vertical axis, and below the line segments.
At each integer value between 0 and 4 on the vertical axis, a horizontal line extends out from the vertical axis to the series of connect line segments.
On the coordinate plane the horizontal axis is labeled x1 and the vertical axis is labeled x2. A region bounded by a series of connected line segments, and several…
Consider the nonlinear optimization model stated below.
Min
s.t.
2x²-18x + 2XY + y² - 14Y + 53
x + 4Y ≤ 8
(a) Find the minimum solution to this problem.
|at (X, Y) =
(b) If the right-hand side of the constraint is increased from 8 to 9, how much do you expect the objective function to change?
Based on the dual value on the constraint X + 4Y ≤ 8, we expect the optimal objective function value to decrease by
(c) Resolve the problem with a new right-hand side of the constraint of 9. How does the actual change compare with your estimate?
If we resolve the problem with a new right-hand-side of 9 the new optimal objective function value is|
, so the actual change is a decrease of
rather than what we expected in part (b).
Chapter 5 Solutions
Finite Mathematics, Books a la Carte Plus MyLab Math Access Card Package (11th Edition)
Ch. 5.1 -
1. What factors determine the amount of interest...Ch. 5.1 - In your own words, describe the maturity value of...Ch. 5.1 -
3. What is meant by the present value of...Ch. 5.1 - We calculated the loan in Example 2(b) assuming...Ch. 5.1 - Find the simple interest. $25,000 at 3% for 9...Ch. 5.1 -
Find the simple interest.
6. $4289 at 4.5% for...Ch. 5.1 -
Find the simple interest.
7. $1974 at 6.3% for...Ch. 5.1 -
Find the simple interest.
8. $6125 at 1.25% for...Ch. 5.1 - Find the simple interest. Assume a 360-day year....Ch. 5.1 -
Find the simple interest. Assume a 360-day...
Ch. 5.1 - Find the maturity value and the amount of simple...Ch. 5.1 - Find the maturity value and the amount of simple...Ch. 5.1 - Find the maturity value and the amount of simple...Ch. 5.1 -
Find the maturity value and the amount of...Ch. 5.1 -
15. Explain the difference between simple...Ch. 5.1 - Prob. 16ECh. 5.1 -
17. What is the difference between t and n?
Ch. 5.1 - In Figure 2, one line is straight and the other is...Ch. 5.1 - Find the compound amount for each deposit and the...Ch. 5.1 -
Find the compound amount for each deposit and...Ch. 5.1 - Prob. 21ECh. 5.1 - Prob. 22ECh. 5.1 - Prob. 23ECh. 5.1 - Find the compound amount for each deposit and the...Ch. 5.1 - Find the interest rate for each deposit and...Ch. 5.1 - Prob. 26ECh. 5.1 -
Find the interest rate for each deposit and...Ch. 5.1 - Prob. 28ECh. 5.1 - Prob. 29ECh. 5.1 - Find the effective rate corresponding to each...Ch. 5.1 -
Find the effective rate corresponding to each...Ch. 5.1 - Prob. 32ECh. 5.1 - Prob. 33ECh. 5.1 - Prob. 34ECh. 5.1 - Find the present value (the amount that should be...Ch. 5.1 - Prob. 36ECh. 5.1 - Prob. 37ECh. 5.1 - Prob. 38ECh. 5.1 -
Find the present value (the amount that should...Ch. 5.1 - Prob. 40ECh. 5.1 - Prob. 41ECh. 5.1 - Prob. 42ECh. 5.1 - Prob. 43ECh. 5.1 - Prob. 44ECh. 5.1 -
Find the doubling time for each of the...Ch. 5.1 - Prob. 46ECh. 5.1 - Prob. 47ECh. 5.1 - Prob. 48ECh. 5.1 - Prob. 49ECh. 5.1 -
50. Delinquent Taxes An accountant for a...Ch. 5.1 - Savings A $1500 certificate of deposit held for 75...Ch. 5.1 - Prob. 52ECh. 5.1 - Cash Advance Fees According to an advertisement,...Ch. 5.1 - Prob. 54ECh. 5.1 - Investments Suppose $10,000 is invested at an...Ch. 5.1 -
56. Investments In Exercise 55, notice that as...Ch. 5.1 - Prob. 57ECh. 5.1 - Prob. 58ECh. 5.1 - Student Loan Upon graduation from college, Warren...Ch. 5.1 - Comparing Investments Two partners agree to invest...Ch. 5.1 - Prob. 61ECh. 5.1 - Prob. 62ECh. 5.1 - Negative Interest Under certain conditions, Swiss...Ch. 5.1 -
Negative Interest Under certain conditions,...Ch. 5.1 - Savings On January 1, 2010, Jack deposited $1000...Ch. 5.1 - Prob. 66ECh. 5.1 - Prob. 67ECh. 5.1 - Prob. 68ECh. 5.1 - Prob. 69ECh. 5.1 -
70. Effective Rate Determine the effective...Ch. 5.1 - Prob. 71ECh. 5.1 - Prob. 72ECh. 5.1 - Buying a House Cara Tilley wants to have $30,000...Ch. 5.1 - Prob. 74ECh. 5.1 -
Doubling Time Use the ideas from Example 11 to...Ch. 5.1 - Prob. 76ECh. 5.1 - Prob. 77ECh. 5.1 - Prob. 78ECh. 5.1 - Prob. 79ECh. 5.1 - Prob. 80ECh. 5.2 - Find the fifth term of each geometric sequence. a...Ch. 5.2 - Prob. 2ECh. 5.2 - Prob. 3ECh. 5.2 - Prob. 4ECh. 5.2 - Find the fifth term of each geometric sequence. a...Ch. 5.2 -
Find the fifth term of each geometric...Ch. 5.2 -
Find the fifth term of each geometric...Ch. 5.2 - Prob. 8ECh. 5.2 - Prob. 9ECh. 5.2 -
Find the sum of the first four terms for each...Ch. 5.2 - Prob. 11ECh. 5.2 - Prob. 12ECh. 5.2 - Prob. 13ECh. 5.2 - Prob. 14ECh. 5.2 - Find the sum of the first four terms for each...Ch. 5.2 - Prob. 16ECh. 5.2 - Prob. 17ECh. 5.2 - Prob. 18ECh. 5.2 - Prob. 19ECh. 5.2 - Find the future value of each ordinary annuity....Ch. 5.2 - Prob. 21ECh. 5.2 -
Find the future value of each ordinary annuity,...Ch. 5.2 -
Find the future value of each ordinary annuity,...Ch. 5.2 - Prob. 24ECh. 5.2 - Find the future value of each ordinary annuity, if...Ch. 5.2 - Prob. 26ECh. 5.2 -
Find the future value of each ordinary annuity,...Ch. 5.2 - Prob. 28ECh. 5.2 - Determine the interest rate needed to accumulate...Ch. 5.2 - Determine the interest rate needed to accumulate...Ch. 5.2 -
Find the periodic payment that will amount to...Ch. 5.2 - Prob. 32ECh. 5.2 - Prob. 33ECh. 5.2 -
Find the amount of each payment to be made into...Ch. 5.2 - Find the amount of each payment to be made into a...Ch. 5.2 - Prob. 36ECh. 5.2 - Prob. 37ECh. 5.2 - Prob. 38ECh. 5.2 -
Find the future value of each annuity due....Ch. 5.2 - Find the future value of each annuity due. Assume...Ch. 5.2 - Prob. 41ECh. 5.2 - Prob. 42ECh. 5.2 - Prob. 43ECh. 5.2 - Prob. 44ECh. 5.2 - Find the future value of each annuity due. Then...Ch. 5.2 - Prob. 46ECh. 5.2 - Prob. 47ECh. 5.2 - Prob. 48ECh. 5.2 - Prob. 49ECh. 5.2 -
50. Retirement Planning A 45-year-old man puts...Ch. 5.2 -
51. Retirement Planning At the end of each...Ch. 5.2 - Prob. 52ECh. 5.2 - Prob. 53ECh. 5.2 - Prob. 54ECh. 5.2 - Individual Retirement Accounts Suppose a...Ch. 5.2 - Prob. 56ECh. 5.2 - Prob. 57ECh. 5.2 - Prob. 58ECh. 5.2 - Prob. 59ECh. 5.2 - Savings A father opened a savings account for his...Ch. 5.2 - Prob. 61ECh. 5.2 - Savings Nic Daubenmire deposits $10,000 at the...Ch. 5.2 - Prob. 63ECh. 5.2 - Prob. 64ECh. 5.2 - Lottery In a 1992 Virginia lottery, the jackpot...Ch. 5.2 - Prob. 66ECh. 5.2 - Prob. 67ECh. 5.2 - Prob. 68ECh. 5.3 - Explain the difference between the present value...Ch. 5.3 -
2. What does it mean to amortize a loan?
Ch. 5.3 - Prob. 3ECh. 5.3 - Find the present value of each ordinary annuity....Ch. 5.3 -
Find the present value of each ordinary...Ch. 5.3 -
Find the present value of each ordinary...Ch. 5.3 - Find the present value of each ordinary annuity....Ch. 5.3 -
Find the present value of each ordinary...Ch. 5.3 - Find the lump sum deposited today that will yield...Ch. 5.3 - Find the lump sum deposited today that will yield...Ch. 5.3 - Find (a) the payment necessary to amortize each...Ch. 5.3 -
Find (a) the payment necessary to amortize each...Ch. 5.3 -
Find (a) the payment necessary to amortize each...Ch. 5.3 - Find (a) the payment necessary to amortize each...Ch. 5.3 -
Find (a) the payment necessary to amortize each...Ch. 5.3 -
Find (a) the payment necessary to amortize each...Ch. 5.3 -
Suppose that in the loans described in Exercises...Ch. 5.3 -
Suppose that in the loans described in Exercises...Ch. 5.3 - Suppose that in the loans described in Exercises...Ch. 5.3 -
Suppose that in the loans described in Exercises...Ch. 5.3 - Prob. 21ECh. 5.3 - Prob. 22ECh. 5.3 - Prob. 23ECh. 5.3 - Prob. 24ECh. 5.3 - What sum deposited today at 5% compounded annually...Ch. 5.3 - What lump sum deposited today at 8% compounded...Ch. 5.3 - Prob. 27ECh. 5.3 - Prob. 28ECh. 5.3 - Prob. 29ECh. 5.3 - Find the monthly house payments necessary to...Ch. 5.3 - Prob. 31ECh. 5.3 -
Suppose that in the loans described in Exercise...Ch. 5.3 -
Suppose that in the loans described in Exercise...Ch. 5.3 - Prob. 34ECh. 5.3 - House Payments Calculate the monthly payment and...Ch. 5.3 - Prob. 36ECh. 5.3 - Prob. 37ECh. 5.3 - Prob. 38ECh. 5.3 - Prob. 39ECh. 5.3 -
40. New Car Financing In 2014, some dealers...Ch. 5.3 - Prob. 41ECh. 5.3 - Prob. 42ECh. 5.3 - Prob. 43ECh. 5.3 - Prob. 44ECh. 5.3 - Installment Buying In Exercises 44-46, prepare an...Ch. 5.3 - Prob. 46ECh. 5.3 - Prob. 47ECh. 5.3 - Prob. 48ECh. 5.3 - House Payments Jason Hoffa buys a house for...Ch. 5.3 -
50. House Payments The Chavara family buys a...Ch. 5.3 - Prob. 51ECh. 5.3 - Prob. 52ECh. 5.3 - Prob. 53ECh. 5.3 - Prob. 54ECh. 5.3 - Prob. 55ECh. 5.3 - Prob. 56ECh. 5.3 - Prob. 57ECh. 5 - Lorri Morgan received $50 on her 16th birthday,...Ch. 5 - At the beginning of the year, Yvette Virgil...Ch. 5 - Prob. 3EACh. 5 - Prob. 4EACh. 5 - People often lose money on investments. Karen...Ch. 5 - Prob. 1RECh. 5 - Prob. 2RECh. 5 - Prob. 3RECh. 5 - Prob. 4RECh. 5 - Prob. 5RECh. 5 - Prob. 6RECh. 5 - Prob. 7RECh. 5 - Prob. 8RECh. 5 - Prob. 9RECh. 5 - Prob. 10RECh. 5 - Prob. 11RECh. 5 - Find the simple interest for each loan. $4902 at...Ch. 5 - Prob. 13RECh. 5 - Prob. 14RECh. 5 - Prob. 15RECh. 5 - Prob. 16RECh. 5 - Prob. 17RECh. 5 -
Find the compound amount in each loan.
18....Ch. 5 - Prob. 19RECh. 5 - Prob. 20RECh. 5 - Prob. 21RECh. 5 -
Find the amount of interest earned by each...Ch. 5 - Find the amount of interest earned by each...Ch. 5 - Prob. 24RECh. 5 - Prob. 25RECh. 5 - Find the present value of each amount. $17,650 in...Ch. 5 - Prob. 27RECh. 5 - Prob. 28RECh. 5 - Prob. 29RECh. 5 - Prob. 30RECh. 5 - Prob. 31RECh. 5 - Prob. 32RECh. 5 - Prob. 33RECh. 5 - Prob. 34RECh. 5 - Prob. 35RECh. 5 - Prob. 36RECh. 5 - Prob. 37RECh. 5 - Prob. 38RECh. 5 - Find the future value of each annuity and the...Ch. 5 -
Find the future value of each annuity and the...Ch. 5 - Prob. 41RECh. 5 - Prob. 42RECh. 5 - Prob. 43RECh. 5 - Prob. 44RECh. 5 - Prob. 45RECh. 5 -
Find the amount of each payment that must be...Ch. 5 - Prob. 47RECh. 5 - Prob. 48RECh. 5 - Prob. 49RECh. 5 -
Find the present value of each ordinary...Ch. 5 - Prob. 51RECh. 5 - Prob. 52RECh. 5 - Find the present value of each ordinary annuity....Ch. 5 - Prob. 54RECh. 5 - Find the amount of the payment necessary to...Ch. 5 - Prob. 56RECh. 5 - Prob. 57RECh. 5 - Prob. 58RECh. 5 - Prob. 59RECh. 5 - Prob. 60RECh. 5 - Prob. 61RECh. 5 - Prob. 62RECh. 5 - Prob. 63RECh. 5 - Personal Finance Carla Truss owes $5800 to her...Ch. 5 - Business Financing Candice Cotton needs to borrow...Ch. 5 - Prob. 66RECh. 5 - Business Investment A developer deposits $84,720...Ch. 5 - Prob. 68RECh. 5 - Prob. 69RECh. 5 - Prob. 70RECh. 5 - Prob. 71RECh. 5 - Prob. 72RECh. 5 - Business Financing The owner of Eastside Hallmark...Ch. 5 - Personal Finance To buy a new computer, David Berg...Ch. 5 - Prob. 75RECh. 5 - Prob. 76RECh. 5 - Prob. 77RECh. 5 -
78. New Car In Spring 2014, some dealers...Ch. 5 - Buying and Selling a House The Bahary family...Ch. 5 - Prob. 80RECh. 5 - Prob. 81RE
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