Operations Research : Applications and Algorithms
Operations Research : Applications and Algorithms
4th Edition
ISBN: 9780534380588
Author: Wayne L. Winston
Publisher: Brooks Cole
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You wish to drive from point A to point B along a highway minimizing the time that you are stopped for gas. You are told beforehand the capacity C of you gas tank in liters, your rate F of fuel consumption in liters/kilometer, the rate r in liters/minute at which you can fill your tank at a gas station, and the locations A = x1, ··· , B = xn of the gas stations along the highway. So if you stop to fill your tank from 2 liters to 8 liters, you would have to stop for 6/r minutes. Consider the following two algorithms: (a) Stop at every gas station, and fill the tank with just enough gas to make it to the next gas station. (b) Stop if and only if you don’t have enough gas to make it to the next gas station, and if you stop,fill the tank up all the way. For each algorithm either prove or disprove that this algorithm correctly solves the problem. Your proof of correctness must use an exchange argument.
At the beginning of the first day (day 1) after grape harvesting is completed, a grapegrower has 8000 kg of grapes in storage. At the end of day n, for n = 1, 2, . . . , the grape grower sells 250n/(n + 1) kg of their stored grapes at the local market at the price of $1.50 per kg.During each day the stored grapes dry out a little so that their weight decreases by 2%.Let wn be the weight (in kg) of the stored grapes at the beginning of day n for n ≥ 1.Find a recursive definition for wn. Draw a timeline. Find the value of wn for n = 1, 2, 3. Let rn be the total revenue (in dollars) earned from the stored grapes from the beginning of day 1 up to the beginning of day n for n ≥ 1.Write a program to compute wn and rn for n = 1, 2, . . . , num where num is entered by the user, and display the values in three columns: n, wn, rn with appropriate headings.Run the program for num = 20. (Use format bank.) Use  program to determine how many days it will take to sell all of the grapes.//This is all…
1. Prove the following formulas log X < X for all X > 0

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Operations Research : Applications and Algorithms

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Operations Research : Applications and Algorithms
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ISBN:9780534380588
Author:Wayne L. Winston
Publisher:Brooks Cole