Mathematics Homework Solutions

Resource Allocation Problem

I worked the attached Resource Allocation Problem, but I am not sure I worked it correctly. I used intuition more than mathematical constructs. Will you take a look and let me know know the right way to do the problem?

Probabilstic Dynamic Programming

The attachted file has an example problem my professor gave. I am not sure that I have it set up right.

Optimal Policy Problem

My professor gave us the solution to one of our homework problems, and I don't understand. The attached file contains his solution, and my questions in red. Can you please help me to understand? A vendor sells sweatshirts at football games. They are equally likely (0.5,0.5) to sell 200 or 400 sweatshirts per game. Each or ...continues

I have a dynamic programming that I don't think I have set up correctly

The attached file contains a dynamic problem. I don't think I have it set up right because I keep going in circles when I attempt to solve it. Could you please help me? I am not sure where I am making my mistake.

Policy Iteration : Probability Distribution and Maximizing Profit

Please see the attached file for the fully formatted problems. 1. A machine in excellent condition earns $100 profit per week, a machine in good condition earns $70 per week, and a machine in poor condition earns $20 per week. At the beginning of any week a machine can be sent out for repairs at a cost of $90. A machine s ...continues

Game Theory : Two-person, Constant-Sum Games

The attached file has a problem that I can't figure out how to set up. Can you take a look and explain how this problem should be set up? There are two people playing a two-person constant-sum game. Player 1 wants to travel from New York to Dallas using the shortest of the possible routes listed below. Player 2 has the ab ...continues

Game Theory : Optimal Strategy for a 2-Person Zero-Sum Game using Mixed Strategies

Find the value and the optimal strategies for the two person zero-sum game below. Player 2 Player 1 1 2 3 2 0 3 I have determined the value of the game, but I don't know how to get to the optimal strategy. Please step through. My professor gave us the answer: Row Player Value = 4/3, The optimal strategy for the ro ...continues

Game Theory : Two-Person Zero-Sum 2 x 3 Matrix (Mixed Strategies)

My problem is attached. I know how to work problems if the matrix is 2x2, but other sizes of matrices confuse me. Can you help? Find the value and the optimal strategies for the two person zero-sum game below. Player 2 Player 1 2 1 3 4 3 2

Simplex Method : Find the Maximum Profit

A brewery manufactures three types of beer - lite, regular, and dark. Each vat of lite beer requires 6 bags of barley, 1 bag of sugar, and 1 bag of hops. Each vat of regular beer requires 4 bags of barlet, 3 bags of sugar and 1 bag of hops. Each vat of dark beer requires 2 bags of barley, 2 bags of sugar and 4 bags of hops. Each ...continues

Game Theory : Two-Person Zero-Sum Game - Find Optimal Strategy

Please see the attached file for the fully formatted problems. Find each player’s optimal strategy and the value of the two-person zero-sum game in Table 31. Player 2 Row Min Player 1 4 5 1 4 1 2 1 6 3 1 1 0 0 2 0 Column Max 4 5 6 4

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