Mathematics For Machine Technology
8th Edition
ISBN: 9781337798310
Author: Peterson, John.
Publisher: Cengage Learning,
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Chapter 40, Problem 2A
To determine
The combination of gage blocks.
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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 ₁ - 2x2+x34x4
subject to 2x1+x22x3x41,
5x1 + x2-x3-×4 ≤ −1,
2x1+x2-x3-34
2,
1, 2, 3, 40.
9. An elementary single period market model contains a risk-free asset with interest rate
r = 5% and a risky asset S which has price 30 at time t = 0 and will have either price
10 or 60 at time t = 1. Find a replicating strategy for a contingent claim with payoff
h(S₁) = max(20 - S₁, 0) + max(S₁ — 50, 0).
Total [8 Marks]
8. An elementary single period market model has a risky asset with price So = 20 at the
beginning and a money market account with interest rate r = 0.04 compounded only
once at the end of the investment period.
=
=
In market model A, S₁ 10 with 15% probability and S₁
21 with 85% probability.
In market model B, S₁ = 25 with 10% probability and S₁ = 30 with 90% probability.
For each market model A, B, determine if the model is arbitrage-free. If not, construct
an arbitrage.
Total [9 Marks]
Chapter 40 Solutions
Mathematics For Machine Technology
Ch. 40 - Prob. 1ACh. 40 - Prob. 2ACh. 40 - Prob. 3ACh. 40 - Prob. 4ACh. 40 - Measure the length of the line segment in Figure...Ch. 40 - Prob. 6ACh. 40 - In Exercises 7 and 8, refer to the number scale in...Ch. 40 - In Exercises 7 and 8, refer to the number scale in...Ch. 40 - In Exercises 9 and 10, select the greater of the...Ch. 40 - In Exercises 9 and 10, select the greater of the...
Ch. 40 - List the following signed numbers in order of...Ch. 40 - Express each of the following pairs of signed...Ch. 40 - Note: For Exercises 13 through 62 that follow,...Ch. 40 - Note: For Exercises 13 through 62 that follow,...Ch. 40 - Note: For Exercises 13 through 62 that follow,...Ch. 40 - Note: For Exercises 13 through 62 that follow,...Ch. 40 - In Exercises 17 through 20, subtract the following...Ch. 40 - In Exercises 17 through 20, subtract the following...Ch. 40 - In Exercises 17 through 20, subtract the following...Ch. 40 - In Exercises 17 through 20, subtract the following...Ch. 40 - In Exercises 17 through 20, subtract the following...Ch. 40 - In Exercises 21 through 24, multiply the following...Ch. 40 - In Exercises 21 through 24, multiply the following...Ch. 40 - Prob. 24ACh. 40 - In Exercises 25 through 28, divide the following...Ch. 40 - In Exercises 25 through 28, divide the following...Ch. 40 - In Exercises 25 through 28, divide the following...Ch. 40 - In Exercises 25 through 28, divide the following...Ch. 40 - In Exercises 29 through 32, raise the following...Ch. 40 - Prob. 30ACh. 40 - In Exercises 29 through 32, raise the following...Ch. 40 - Prob. 32ACh. 40 - Prob. 33ACh. 40 - In Exercises 33 through 36, determine the...Ch. 40 - Prob. 35ACh. 40 - Prob. 36ACh. 40 - Prob. 37ACh. 40 - Prob. 38ACh. 40 - Prob. 39ACh. 40 - Solve each of the following problems using the...Ch. 40 - Prob. 41ACh. 40 - Prob. 42ACh. 40 - Solve each of the following problems using the...Ch. 40 - Solve each of the following problems using the...Ch. 40 - Prob. 45ACh. 40 - Solve each of the following problems using the...Ch. 40 - Prob. 47ACh. 40 - Solve each of the following problems using the...Ch. 40 - Prob. 49ACh. 40 - Prob. 50ACh. 40 - Prob. 51ACh. 40 - Prob. 52ACh. 40 - Substitute the given numbers for letters in the...Ch. 40 - Substitute the given numbers for letters in the...Ch. 40 - Substitute the given numbers for letters in the...Ch. 40 - Substitute the given numbers for letters in the...Ch. 40 - Substitute the given numbers for letters in the...Ch. 40 - Substitute the given numbers for letters in the...Ch. 40 - Substitute the given numbers for letters in the...Ch. 40 - Substitute the given numbers for letters in the...Ch. 40 - Substitute the given numbers for letters in the...Ch. 40 - Substitute the given numbers for letters in the...
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- 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 ₁ - 2x2+x34x4 subject to 2x1+x22x3x41, 5x1 + x2-x3-×4 ≤ −1, 2x1+x2-x3-34 2, 1, 2, 3, 40.arrow_forwardSuppose we have a linear program in standard equation form maximize cTx 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.arrow_forwarda) 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 x2 x3 81 82 83 84 81 -2 0 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 -8arrow_forward
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- Find the closed formula for each of the following sequences (a_n)_n>=1 by realting them to a well known sequence. Assume the first term given is a_1 d. 5,23,119,719,5039 i have tried finding the differnces and the second difference and i still dont see the patternarrow_forwardYou 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.arrow_forwarda) 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.arrow_forward
- 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.arrow_forward(a) For the following linear programme, sketch the feasible region and the direction of the objective function. Use you sketch to find an optimal solution to the program. State the optimal solution and give the objective value for this solution. maximize +22 subject to 1 + 2x2 ≤ 4, 1 +3x2 ≤ 12, x1, x2 ≥0 (b) For the following linear programme, sketch the feasible region and the direction of the objective function. Explain, making reference to your sketch, why this linear programme is unbounded. maximize ₁+%2 subject to -2x1 + x2 ≤ 4, x1 - 2x2 ≤4, x1 + x2 ≥ 7, x1,x20 Give any feasible solution to the linear programme for which the objective value is 40 (you do not need to justify your answer).arrow_forwardfind the domain of the function f(x)arrow_forward
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