Solving sudoku as an Integer Programming problem
... problem ⊡ A standard way to solve sudoku is by applying recursion, an algorithm where the solution depends on solutions to smaller instances of the reference problem. One checks all the combinations (for every cell it considers all integers between 1 and 9) and stops when finding a solution which sa ...
... problem ⊡ A standard way to solve sudoku is by applying recursion, an algorithm where the solution depends on solutions to smaller instances of the reference problem. One checks all the combinations (for every cell it considers all integers between 1 and 9) and stops when finding a solution which sa ...
MATH 1390 W12 Quiz 4 Solutions 1 1. Using mathematical
... a State what needs to be proven in the base step. Solution We need to show that P (1) is true; that is, the above equation holds for n = 1. b) Prove the base step. Solution When n = 1, the left side (L.S.) of the equation equals 1. The right side (R.S.) equals 1 · (3 · 1 − 2) = 1. ∴ L.S. = R.S. and ...
... a State what needs to be proven in the base step. Solution We need to show that P (1) is true; that is, the above equation holds for n = 1. b) Prove the base step. Solution When n = 1, the left side (L.S.) of the equation equals 1. The right side (R.S.) equals 1 · (3 · 1 − 2) = 1. ∴ L.S. = R.S. and ...
Weekly Problems Due Math Monday Spirit Days
... Make a model/picture to represent the problem. 3. CARRY OUT THE PLAN Implement the strategy or strategies in step 2, and perform any necessary actions or computations. Check each step of the plan as you proceed. This may be intuitive checking or formal calculations. Keep an accurate record o ...
... Make a model/picture to represent the problem. 3. CARRY OUT THE PLAN Implement the strategy or strategies in step 2, and perform any necessary actions or computations. Check each step of the plan as you proceed. This may be intuitive checking or formal calculations. Keep an accurate record o ...
Persuasive Speech Critique
... development of the process but needs to go further; ( ) very little, if any evidence of something to capture our attention at the onset of the speech ...
... development of the process but needs to go further; ( ) very little, if any evidence of something to capture our attention at the onset of the speech ...
CPSC 121 - MATHEMATICAL PROOFS 1. Proofs in General
... Definition. The floor function assigns to the real number x the largest integer that is less than or equal to x. In other words, the floor function rounds a real number down to the nearest integer. The value of the floor function is denoted by bxc. Definition. The ceiling function assigns to the rea ...
... Definition. The floor function assigns to the real number x the largest integer that is less than or equal to x. In other words, the floor function rounds a real number down to the nearest integer. The value of the floor function is denoted by bxc. Definition. The ceiling function assigns to the rea ...
Multiple-criteria decision analysis
Multiple-criteria decision-making or multiple-criteria decision analysis (MCDA) is a sub-discipline of operations research that explicitly considers multiple criteria in decision-making environments. Whether in our daily lives or in professional settings, there are typically multiple conflicting criteria that need to be evaluated in making decisions. Cost or price is usually one of the main criteria. Some measure of quality is typically another criterion that is in conflict with the cost. In purchasing a car, cost, comfort, safety, and fuel economy may be some of the main criteria we consider. It is unusual that the cheapest car is the most comfortable and the safest one. In portfolio management, we are interested in getting high returns but at the same time reducing our risks. Again, the stocks that have the potential of bringing high returns typically also carry high risks of losing money. In a service industry, customer satisfaction and the cost of providing service are two conflicting criteria that would be useful to consider.In our daily lives, we usually weigh multiple criteria implicitly and we may be comfortable with the consequences of such decisions that are made based on only intuition. On the other hand, when stakes are high, it is important to properly structure the problem and explicitly evaluate multiple criteria. In making the decision of whether to build a nuclear power plant or not, and where to build it, there are not only very complex issues involving multiple criteria, but there are also multiple parties who are deeply affected from the consequences.Structuring complex problems well and considering multiple criteria explicitly leads to more informed and better decisions. There have been important advances in this field since the start of the modern multiple-criteria decision-making discipline in the early 1960s. A variety of approaches and methods, many implemented by specialized decision-making software, have been developed for their application in an array of disciplines, ranging from politics and business to the environment and energy.