Concept explainers
a.
Feasible region:
A feasible region for an LPP is the set of all points that satisfies the constraints and non-negative restrictions of the corresponding LPP.
Mathematical model of the given LPP:
Subject to the constraints,
b.
Explanation of Solution
Determining feasible region:
Given point:
The points
c.
Explanation of Solution
Determining feasible region:
Given point:
d.
Explanation of Solution
Determining feasible region:
Given point:
The points
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Chapter 3 Solutions
Operations Research : Applications and Algorithms
- 0 1 X process service period P1 7 29 P2 12 25 P3 2 5 2 fill in the gant chart below (until time 20) for the most feasible case (X, Y, or Z) 3 4 5 6 Y process service period P1 8 34 P2 35 90 P3 7 20 7 Z process service period P1 5 22 10 P2 3 P3 7 58 8 9 10 11 12 13 14 15 16 17 18 19 20arrow_forwardGiven the objective function 2x1+5x2 that needs to be maximized and the graphical solution shown below, what is the optimal value of the objective function? 420 20 [ [8] Answer: 45arrow_forwardExplain the relationship between the Bellman equation and the principle of optimality in dynamic programming.arrow_forward
- Calculate solving of the following 0/1 Knapsack Problem Dynamic Programming! n = 7; W = 10; (w1, w2, w3, w4, w5, w6, w7) = (5, 2, 3, 6, 4, 3, 2); (b1, b2, b3, b4, b5, b6, b7) = (36, 16, 21, 57, 28, 24, 13) n = 8; W = 9; (w1, w2, w3, w4, w5, w6, w7) = (5, 2, 3, 2, 6, 2, 4, 3); (b1, b2, b3, b4, b5, b6, b7) = (32, 59, 30, 17, 81, 16, 39, 25)arrow_forwardManually solve the following linear program (which could result from a production problem) following the simplex algorithm. Start from the obvious basic feasible solution of Xb = (X3, X4, X5 ) = (18, 4, 12). You may use excel to carry out calculations in simplex tableau if it helps, but please include all tableaus from all iterations in your submitted work. Maximize: 30 X1 + 50 X2 Subject to: 3X1 +5X2 +X3=18. X1 +X4 =4. 2X2 +X5 =12. X1, X2, X3, X4, X5 >= 0.arrow_forwardWhat is the difference between feasible solution and optimal solution?arrow_forward
- Coding problems: HW5_2 A thin square metal plate has uniform temperature of E1 4T, = E, + E2 + T, + T6 degrees on two opposite edges, a temperature of E2 on one edge, 4T, = E, + T1 + T3 + T5 and E3 on the final edge. Equations can be written for the 4T3 = E1 + E3 +T2+ T4 temperatures, Ti, at 6 uniformly spaced interior nodes. Solve for the 4T4 = E1 + E3 + T3 + T5 node temperatures when E1=80, E2=120 and E3=60. 4T5 = E1 + T2 + T4 + T6 Present the results in a complete sentence using fprintf 4T, = E1 + E2 + T, + T5arrow_forwardAssume you want to run a computer program to derive the efficient frontier for your feasible set of stocks. What information must you input to the program?arrow_forward8. A school is creating class schedules for its students. The students submit their requested courses and then a program will be designed to find the optimal schedule for all students. The school has determined that finding the absolute best schedule cannot be solved in a reasonablo time. Instead they have decided to use a simpler algorithm that produces a good but non-optimal schedule in a more reasonable amount of time. Which principle does this decision best demonstrate? O A Unreasonable algorithms may sometimes also be undecidable O B. Heuristics can be used to solve some problems for which no reasonable algorithm exsts O C. efficiency Two algorithms that solve the same problem must also have the same O B. Approximate solutions are often identical to optimal solutionsarrow_forward
- 8. A school is creating class schedules for its students. The students submit their requested courses and then a program will be designed to find the optimal schedule for all students. The school has determined that finding the absolute best schedule cannot be solved in a reasonable time. Instead they have decided to use a simpler algorithm that produces a good but non-optimal schedule in a more reasonable amount of time. Which principle does this decision best demonstrate? A. Unreasonable algorithms may sometimes also be undecidable B. Heuristics can be used to solve some problems for which no reasonable algorithm exists C. Two algorithms that solve the same problem must also have the same efficiency D. Approximate solutions are often identical to optimal solutions 0000arrow_forwardIn Simulated Annealing, if the current state’s evaluation function value is 15, the selected successor state’s value is 11, and the current temperature is T = 10, what is the probability of moving to the successor state? (Assume we are maximizing the evaluation function.) Please give your answer as either an expression or a number.arrow_forwardUSING PYTHON, verify that the problem: y' = y1/3 y(0) = 0 has two solutions: y = 0 and y = (2x/3)3/2. Which of the solutions would be reproduced by numerical integration if the initial condition is set at (a) y = 0 and (b) y = 10-16? Verify your conclusions by integrating with any numerical method.arrow_forward
- Operations Research : Applications and AlgorithmsComputer ScienceISBN:9780534380588Author:Wayne L. WinstonPublisher:Brooks Cole