Formulate the following question as an integer program: how many non-mutually attacking queenscan you fit into a chessboard? See example in Figure 1. A queen can attack horizontally, vertically,and diagonally, regardless of how far the other piece is on the board. Solve the integer programusing gurobi. Use gurobi to generate at least two distinct ways to position the queens on the boardFigure 1: Non-mutually attacking queens(they must be distinct up to rotation).

import numpy as np import scipy.sparse as sp import gurobipy as gp from gurobipy import grb

Answered: Formulate the following question as an…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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A survey of 145 college students was done to find out what elective courses they were taking. Let A=the set of those taking art, B= the set of those taking basketweaving, and C= the set of those taking canoeing. The study revealed the following information.n(A)= 45n(B)= 55n(C)=40n(AnB)= 12n(AnC)= 15n(BnC)= 23n(AnBnC)= 2 How many students were not taking any of these electives?
a.) Make a list of the amounts of money one can have that cannot be reduced to a smaller number of coins. (Hint: there are seven possible amounts.) One of the amounts is (d+e). b.) Make an addition table for Glosian money. It should be a seven by seven table, with a row and column for each of the amounts you found in the previous problem. For example, your table shouldshow that (d+e)+d=f c.) One of the seven amounts you found in the previous problem can be considered to be the zero of Glosian money, since adding it to a collection of coins does not change the collection’s value (after trading to get the smallest possible number of coins, of course.) Which amount is the zero forGlosian money? d.) The opposite of an amount is the amount you add to it to get the zero. Find the opposite of each of the seven amounts.
Consider a popular ramen stall. Before the shop opens, there are 20people waiting in front of the restaurant. Given that the shop only serves 10 bowls per day. If the maximum number ofeach menu the customers can order is 7 which means if the first 7 people orderShoyu Ramen, the rest must order Seafood Ramen. How many combinationof ramen orders(how each customer order and who got kicked out) are there?Ex: People can still order 5 Shoyu and 5 Seafood if they wish. But, no, the10 people who gets in can’t order 8 Shoyu and 2 Seafood.
Mrs. Smith has 6 activity tables she wants to line up side by side in her classroom. (a) In how many ways can she arrange all 6 tables? Show your work.(b) If she only wants to have 4 of the tables set up, in how many ways can she choose the tables shewishes to have set up? Show your work. Answer:
A 100-page document is being printed by four printers. Each page will be printed exactly once. Suppose that the first and the last page of the document must be printed in color, and only two printers are able to print in color. The two color printers can also print black-and-white. How many ways are there for the 100 pages to be assigned to the four printers. Hint: Use the product rule.
A rectangular board, 3 by 2, is divided into 1 by 1 squares. Each square can be coloured red or black. (Note that if one colouring can be obtained from another by rotation, the two colourings are distinct.) If three squares are red and three are black, in how many ways can the board be coloured?
At the beginning of a game of chess, the back row consists of two (identical) rooks on the corners, then two knights next to them, then two bishops, and finally a king and a queen in the center. Bobby Fischer, an American chess legend, popularized the idea of randomly shuffled starting positions. Inhow many distinct ways can the eight pieces above be aligned?

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