数学代写|MTH390 Operations Research
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MTH390 Operations Research课程简介
Operations Research utlizes mathematical modeling, techniques, and algorithms, to most appropriately allocate resources and meet goals. An alternative title for the course might be “Mathematical Theory of Management, Control and Decision Making” . In general the course is intended for students with interests in applied math, statistics, economics, engineering and science. A second semester of the course devoted to probabilistic techniques will be offered in the spring semester.
PREREQUISITES
Linear programming is a widely-used optimization technique that involves linear objective functions and linear constraints. The simplex algorithm is a widely-used algorithm for solving linear programming problems, and it involves moving from one feasible solution to another in an iterative fashion until an optimal solution is found. Sensitivity analysis involves examining the effects of changes in the objective function coefficients and constraint values on the optimal solution.
Dual problems are closely related to linear programming problems and involve the optimization of a dual objective function subject to dual constraints. The dual problem is used to provide information about the original problem, including bounds on the optimal objective value and information about the shadow prices of the constraints.
Integer programming is a type of linear programming that involves additional constraints that require the variables to take on integer values. Network models involve the modeling of complex systems using networks, such as transportation or communication systems. Dynamic programming is a powerful optimization technique that involves breaking down a problem into smaller subproblems and solving each subproblem in a recursive manner.
Finally, the KKT conditions are a set of necessary conditions for an optimization problem to have an optimal solution. These conditions involve the first-order conditions for optimality and the complementary slackness conditions, and they are used to analyze optimization problems and to derive insights about their solutions.
MTH390 Operations Research HELP(EXAM HELP, ONLINE TUTOR)
(1) The sales manager thinks that it may be possible to increase the profit on product $C$ from 6 euros to 8 euros per unit. What happens to the optimal solution?
(2) The purchasing manager can buy 100 additional units of raw material from another supplier. However, this supplier’s price is 1.50 euros more per unit of raw material than the current supplier’s unit price. It is not possible to buy more raw material from the current supplier. What is the advice?
(3) The customer to whom 100 units of product $A$ had already been promised is willing to cancel the order in exchange for a compensation of 575 euros. What is the advice to the sales manager?
(4) The production manager thinks that 14 production hours can be transferred from finishing to assembly. The cost of this transfer is 140 euros. What are the comments on this?
Textbooks
• An Introduction to Stochastic Modeling, Fourth Edition by Pinsky and Karlin (freely
available through the university library here)
• Essentials of Stochastic Processes, Third Edition by Durrett (freely available through
the university library here)
To reiterate, the textbooks are freely available through the university library. Note that
you must be connected to the university Wi-Fi or VPN to access the ebooks from the library
links. Furthermore, the library links take some time to populate, so do not be alarmed if
the webpage looks bare for a few seconds.
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