do the following code on matlab with the given and specified format Question 2 (25 points):Build a function f(t) that outputs according to the following conditions:f(t) = ln(t + 1)= {ince0; t≤0;0% Initialize f to 0 for all tf=zeros(size(t));for i=1:length(t)f(i) = piecefcn(t(i));end% Plot function here% Piecewise function herefunction [f]=piecefcn(t)% Conditional statement hereend

% Main code clc; clear; % Define t from -1 to 5 with a step size of 0.01 t = -1:0.01:5; %…

Answered: Question 2 (25 points): Build a…

Operations Research : Applications and Algorithms

4th Edition

ISBN:9780534380588

Author:Wayne L. Winston

Publisher:Wayne L. Winston

Chapter20: Queuing Theory

Section20.6: The M/m/s/gd/∞/∞ Queuing System

Problem 1P

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Recall Pigou’s example discussed in class, where there are two roads that connect a source, s, and destination, t. The roads have different travel costs. Fraction x1 of the traffic flow on route 1, and the remainder x2 on route 2. Here consider the following scenario. • The first road has “infinite” capacity but is slow and requires 1 hour travel time, T1 = 1. • The second road always requires at least 15 mins, which then increases as a function of traffic density, T2 = 0.25 + 0.75x2. If drivers act in a “selfish” manner – the user optimal scenario – all the traffic will flow on the second path, as one is never worse off. Worst case scenario for path 2, both paths take one hour. So no one is incentivized to change their behavior. 1. Assume user optimal behavior, and calculate τ the expected travel time per car. 2. If instead we could control the flows, we could minimize the expected travel time. Using the expression in part (a), calculate the optimal allocation of flows x¯1 and ¯x2…
Assume that we have two functions: f(n) and g(n). On a benchmark where n = 10,000, the execution time of f(n) was 15 seconds and the execution time of g(n) was 2.3 seconds. What can we conclude about these two functions?
Answer the following: This problem exercises the basic concepts of game playing, using tic-tac-toe (noughts and crosses) as an example. We define Xn as the number of rows, columns, or diagonals with exactly n X’s and no O’s. Similarly, On is the number of rows, columns, or diagonals with just n O’s. The utility function assigns +1 to any position with X3=1 and −1 to any position with O3=1. All other terminal positions have utility 0. For nonterminal positions, we use a linear evaluation function defined as Eval(s)=3X2(s)+X1(s)−(3O2(s)+O1(s)). a. Show the whole game tree starting from an empty board down to depth 2 (i.e., one X and one O on the board), taking symmetry into account. b. Mark on your tree the evaluations of all the positions at depth 2. c .Using the minimax algorithm, mark on your tree the backed-up values for the positions at depths 1 and 0, and use those values to choose the best starting move. Provide original solutions including original diagram for part a!
Answer the following: This problem exercises the basic concepts of game playing, using tic-tac-toe (noughts and crosses) as an example. We define Xn as the number of rows, columns, or diagonals with exactly n X’s and no O’s. Similarly, On is the number of rows, columns, or diagonals with just n O’s. The utility function assigns +1 to any position with X3=1 and −1 to any position with O3=1. All other terminal positions have utility 0. For nonterminal positions, we use a linear evaluation function defined as Eval(s)=3X2(s)+X1(s)−(3O2(s)+O1(s)). a. Show the whole game tree starting from an empty board down to depth 2 (i.e., one X and one O on the board), taking symmetry into account. b. Mark on your tree the evaluations of all the positions at depth 2. c .Using the minimax algorithm, mark on your tree the backed-up values for the positions at depths 1 and 0, and use those values to choose the best starting move. Provide original solution!
The motorway management perceives that the waiting time computed in (a) above is not acceptable and it wishes to reduce it, first, by adding an extra tollbooth assistant to help improve the service rate to 250 motorists every 8-hour-day. The tollbooth attendant will be paid a monthly salary of GH¢400. The second option is that management can add a toll-operated machine which will cost GH¢3,000 and this amount is a free gift from the Minister. This option will reduce the arrival rate to 35 motorists every 2 hours. However, management will have to pay the operator who will man the toll-operated machine a monthly salary of GH¢550. Whichever option management adopts; they avoid lost sales of GH¢1,200.00 per month for every minute that average waiting time is reduced. Advise management which option it must adopt?
A firm is considering projects A, B, . . . , H. Using binary variables x_a, ..., x_h and linear constraints, model the following conditions on the projects to be undertaken. At most one of A,B,...,H. Exactly two of A,B,...,H. If A then B. If A then not B. If not A then B. If A then B and C. If A then B, and if B then A. If A then B or C. If B or C then A. If B and C then A. If two or more of B,C,D,E then A. If m or more than n projects B,...,H then A.
Simplify the following Boolean functions, using three-variable k-maps: a. F (x,y,z) = Σ(2,3,4,5) b. F (x,y,z) = Σ(0,2,4,6) c. F (x,y,z) = Σ(1,2,3,6,7) d. F (x,y,z) = Σ(1,2,3,5,6,7) e. F (x,y,z) = Σ(3,4,5,6,7)
Consider the following computation problem in two variables Plus: Input -14 <= x <= 28, x ∈ Z; -10 <= y <= 32, y∈ Z Output the integer x+y-7 and the following partition of the input domains: Ax = {[-14,-1], [0,10], [11,18]} for the variable x Ay = {[-10,12], [13, 32]} for the variable y Consider the following test suite: S: Test case x y Expected result T1 -5 5 -7 T2 5 5 3 T3 15 15 23 Say what holds for S: Consider the following computation problem in two variables Plus: Input -14 <= x <= 28, x ∈ Z; -10 <= y <= 32, y∈ Z Output the integer x+y-7 and the following partition of the input domains: Ax = {[-14,-1], [0,10], [11,18]} for the variable x Ay = {[-10,12], [13, 32]} for the variable y Consider the following test suite: S: Test case x y Expected result T1 -5 5 -7 T2 5 5 3 T3 15 15 23 Say what holds for S: a) It has more test…
A contractor owns three excavators of different capacity. He/she wants to dispatch these excavatorsinto three different jobs. The performance of the excavators is measured as the time consumed toperform each job. The data of the time tests are shown as given in the table below. (a) Draw a network flow diagram.(b) Formulate a mathematical model to obtain the minimum time.(c) Solve this model using the Vogel’s approximation model.
This problem exercises the basic concepts of game playing, using tic-tac-toe (noughtsand crosses) as an example. We define Xn as the number of rows, columns, or diagonals with exactly n X’s and no O’s. Similarly, On is the number of rows, columns, or diagonals with just n O’s. The utility function assigns +1 to any position with X3 = 1 and −1 to any position with O3 = 1. All other terminal positions have utility 0. For nonterminal positions, we use a linear evaluation function defined as Eval (s) = 3X2(s)+X1(s)−(3O2(s)+O1(s))."Mark on your tree the evaluations of all the positions at depth 2."
A company manufactures two types of trucks. Each truck must go through the painting shop and the assembly shop. If the painting shop were completely devoted to painting type 1 trucks, 800 per day could be painted, whereas if the painting shop were completely devoted to painting type 2 trucks, 700 per day could be painted. If the assembly shop were completely devoted to assembling truck 1 engines, 1500 per day could be assembled, whereas if the assembly shop were completely devoted to assembling truck 2 engines, 1200 per day could be assembled. It is possible, however, to paint both types of trucks in the painting shop. Similarly, it is possible to assemble both types in the assembly shop. Each type 1 truck contributes $1000 to profit; each type 2 truck contributes $1500. Use Solver to maximize the company’s profit
6. Consider a modification to the rod-cutting problem in which, in addition to a value pi for each rod, there is handling cost ci that is one and a half times the length of the rod cut plus a flat fee of 3 (i.e., the handling cost to cut a rod of length 5 is 7.5+3 =10). The revenue generated is the sum of the value of the pieces cut minus the sum of handling costs of the cuts. Provide a dynamic programming approach to solve this problem given an initial rod of length n with potential cut lengths of 1, 2, 5, and 7 [Adapted from ITA, pg. 370, 15.1-3] length of cut (i) 1 2 5 7 value (pi) 5 7 30 45 handling cost (ci) 4.5 6 10.5 13.5

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