Numerous engineering and scientific applications require finding solutions to a set of equations. Ex: 8x + 7y = 38 and 3x - 5y = -1 have a solution x = 3, y = 2. Given integer coefficients of two linear equations with variables x and y, use brute force to find an integer solution for x and y in the range -10 to 10. Ex: If the input is: 8 7 38 3 -5 -1 then the output is: 3 2 Use this brute force approach: For every value of x from -10 to 10 For every value of y from -10 to 10 Check if the current x and y satisfy both equations. If so, output the solution, and finish. Ex: If no solution is found, output: No solution You can assume the two equations have no more than one solution. Note: Elegant mathematical techniques exist to solve such linear equations. However, for other kinds of equations or situations, brute force can be handy.

Numerous engineering and scientific applications require finding solutions to a set of equations. Ex: 8x + 7y = 38 and 3x - 5y = -1 have a solution x = 3, y = 2. Given integer coefficients of two linear equations with variables x and y, use brute force to find an integer solution for x and y in the range -10 to 10. Ex: If the input is: 8 7 38 3 -5 -1 then the output is: 3 2 Use this brute force approach: For every value of x from -10 to 10 For every value of y from -10 to 10 Check if the current x and y satisfy both equations. If so, output the solution, and finish. Ex: If no solution is found, output: No solution You can assume the two equations have no more than one solution. Note: Elegant mathematical techniques exist to solve such linear equations. However, for other kinds of equations or situations, brute force can be handy.

Operations Research : Applications and Algorithms

4th Edition

ISBN:9780534380588

Author:Wayne L. Winston

Publisher:Wayne L. Winston

Chapter23: Simulation With The Excel Add-in @risk

Section: Chapter Questions

Problem 9RP

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Numerous engineering and scientific applications require finding solutions to a set of equations. Ex: 8x + 7y = 38 and 3x - 5y = -1 have a solution x = 3, y = 2. Given integer coefficients of two linear equations with variables x and y, use brute force to find an integer solution for x and y in the range -10 to 10. Ex: If the input is: 8 7 38 3 -5 -1 Then the output is: x = 3 , y = 2 Use this brute force approach: For every value of x from -10 to 10 For every value of y from -10 to 10 Check if the current x and y satisfy both equations. If so, output the solution, and finish. Ex: If no solution is found, output: There is no solution You can assume the two equations have no more than one solution. Note: Elegant mathematical techniques exist to solve such linear equations. However, for other kinds of equations or situations, brute force can be handy. ''' Read in first equation, ax + by = c '''a = int(input())b = int(input())c = int(input()) ''' Read in second equation, dx + ey = f '''d…
Numerous engineering and scientific applications require finding solutions to a set of equations. Ex: 8x + 7y = 38 and 3x - 5y = -1 have a solution x = 3, y = 2. Given integer coefficients of two linear equations with variables x and y, use brute force to find an integer solution for x and y in the range -10 to 10. Ex: If the input is: 8 7 38 3 -5 -1 Then the output is: x = 3 , y = 2 Use this brute force approach: For every value of x from -10 to 10 For every value of y from -10 to 10 Check if the current x and y satisfy both equations. If so, output the solution, and finish. Ex: If no solution is found, output: There is no solution You can assume the two equations have no more than one solution. Note: Elegant mathematical techniques exist to solve such linear equations. However, for other kinds of equations or situations, brute force can be handy. What is the code in python?
In C++ Numerous engineering and scientific applications require finding solutions to a set of equations. Ex: 8x + 7y = 38 and 3x - 5y = -1 have a solution x = 3, y = 2. Given integer coefficients of two linear equations with variables x and y, use brute force to find an integer solution for x and y in the range -10 to 10. Ex: If the input is: 8 7 383 -5 -1 the output is: x = 3, y = 2 Use this brute force approach: For every value of x from -10 to 10 For every value of y from -10 to 10 Check if the current x and y satisfy both equations. If so, output the solution, and finish. Ex: If no solution is found, output: There is no solution You can assume the two equations have no more than one solution. Note: Elegant mathematical techniques exist to solve such linear equations. However, for other kinds of equations or situations, brute force can be handy. #include <iostream>using namespace std; int main() { /* Type your code here. */ return 0;}
(Python) Numerous engineering and scientific applications require finding solutions to a set of equations. Ex: 8x + 7y = 38 and 3x - 5y = -1 have a solution x = 3, y = 2. Given integer coefficients of two linear equations with variables x and y, use brute force to find an integer solution for x and y in the range -10 to 10. Ex: If the input is: 8 7 38 3 -5 -1 Then the output is: x = 3 , y = 2 Use this brute force approach: For every value of x from -10 to 10 For every value of y from -10 to 10 Check if the current x and y satisfy both equations. If so, output the solution, and finish. Ex: If no solution is found, output: "There is no solution" You can assume the two equations have no more than one solution. ''' Read in first equation, ax + by = c '''a = int(input())b = int(input())c = int(input()) ''' Read in second equation, dx + ey = f '''d = int(input())e = int(input())f = int(input())
Consider the problem of making change for n cents using the fewest number of coins. Assume that we live in a country where coins come in k dierent denominations c1, c2, . . . , ck, such that the coin values are positive integers, k ≥ 1, and c1 = 1, i.e., there are pennies, so there is a solution for every value of n. For example, in case of the US coins, k = 4, c1 = 1, c2 = 5, c3 = 10, c4 = 25, i.e., there are pennies, nickels, dimes, and quarters. To give optimal change in the US for n cents, it is sufficient to pick as many quarters as possible, then as many dimes as possible, then as many nickels as possible, and nally give the rest in pennies. Design a bottom-up (non-recursive) O(nk)-time algorithm that makes change for any set of k different coin denominations. Write down the pseudocode and analyze its running time. Argue why your choice of the array and the order in which you fill in the values is the correct one. Notice how it is a lot easier to analyze the running time of…
Consider the problem of making change for n cents using the fewest number of coins. Assume that we live in a country where coins come in k dierent denominations c1, c2, . . . , ck, such that the coin values are positive integers, k ≥ 1, and c1 = 1, i.e., there are pennies, so there is a solution for every value of n. For example, in case of the US coins, k = 4, c1 = 1, c2 = 5, c3 = 10, c4 = 25, i.e., there are pennies, nickels, dimes, and quarters. To give optimal change in the US for n cents, it is sufficient to pick as many quarters as possible, then as many dimes as possible, then as many nickels as possible, and nally give the rest in pennies. Design a bottom-up (non-recursive) O(nk)-time algorithm that makes change for any set of k different coin denominations. Write down the pseudocode and analyze its running time. Argue why your choice of the array and the order in which you ll in the values is the correct one.
Consider the problem of making change for n cents using the fewest number of coins. Assume that we live in a country where coins come in k dierent denominations c1, c2, . . . , ck, such that the coin values are positive integers, k ≥ 1, and c1 = 1, i.e., there are pennies, so there is a solution for every value of n. For example, in case of the US coins, k = 4, c1 = 1, c2 = 5, c3 = 10, c4 = 25, i.e., there are pennies, nickels, dimes, and quarters. To give optimal change in the US for n cents, it is sufficient to pick as many quarters as possible, then as many dimes as possible, then as many nickels as possible, and nally give the rest in pennies. Prove that the coin changing problem exhibits optimal substructure. Design a recursive backtracking (brute-force) algorithm that returns the minimum number of coins needed to make change for n cents for any set of k different coin denominations. Write down the pseudocode and prove that your algorithm is correct.
We examine a problem in which we are handed a collection of coins and are tasked with forming a sum of money n out of the coins. The currency numbers are coins = c1, c2,..., ck, and each coin can be used as many times as we want. What is the bare amount of money required?If the coins are the euro coins (in euros) 1,2,5,10,20,50,100,200 and n = 520, we need at least four coins. The best option is to choose coins with sums of 200+200+100+20.
Let l be a line in the x-y plane. If l is a vertical line, its equation is x 5a for some real number a. Suppose l is not a vertical line and its slope is m. Then the equation of l is y 5mx 1b, where b is the y-intercept. If l passes through the point (x0, y0,), the equation of l can be written as y 2y0 5m(x 2x0 ). If (x1, y1) and (x2, y2) are two points in the x-y plane and x1 ≠ x2, the slope of line passing through these points is m 5(y2 2y1 )/(x2 2x1 ). Write a program that prompts the user two points in the x-y plane. The program outputs the equation of the line and uses if statements to determine and output whether the line is vertical, horizontal, increasing, or decreasing. If l is a non-vertical line, output its equation in the form y 5mx 1b.
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…
Consider the following bridge crossing problem where n people with speeds s1, ··· , sn wish to cross the bridge as quickly as possible. The rules remain: • It is nighttime and you only have one flashlight. • A maximum of two people can cross at any one time • Any party who crosses, either 1 or 2 people must have the flashlight with them. • The flashlight must be walked back and forth, it cannot be thrown, etc. • A pair must walk together at the rate of the slower person’s pace. Give an efficient algorithm to find the fastest way to get a group of people across the bridge. You must have a proof of correctness for your method.
Numerous engineering and scientific applications require finding solutions to a set of equations. Ex: 8x + 7y = 38 and 3x - 5y = -1 have a solution x = 3, y = 2. Given integer coefficients of two linear equations with variables x and y, use brute force to find an integer solution for x and y in the range -10 to 10. program language is c