App MMA Lab 1 - AY11-2 Ski_Slope

App MMA Lab 1 - AY11-2 Ski_Slope - Differential Calculus...

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Unformatted text preview: Differential Calculus MA104 Applied MMA Lab 1 Assignment DUE: InClass on L28 (23 Feb 11) READ THESE INSTRUCTIONS CAREFULLY BEFORE STARTING WORK: 1. This applied Mathematica lab is an individual assignment. Include a cover sheet and document any assistance you receive in accordance with Documentation of Academic Work (June 2010). 2. Your submission will be in the format prescribed in the turnin requirements link on the MA104 webpage and must be typed using Microsoft Word equation editor where appropriate. ______________________________________________________________________________ Scenario: The West Point Ski Slope (WPSS) Director of Operations purchased a new snow system to increase snow making capability for next ski season. Currently, WPSS has the ability to make snow for only one of the two main ski runs and the bunny slope simultaneously. This new system will allow for concurrent snow making on both main trails. Snow is created by utilizing a compressor that shoots a pressurized air/water mix into the cold air. The manufacture states that the most consistent snow is created when water pressure ranges between 69 and 76.5 psi (pounds per square inch). The manufacturer also provided the following function that models the rate of water usage: 1,863,863,661 130,653,224 3,660,014 51,216 358 , where p is the pressure of the water. The WPSS's net cost of water is $0.097 per gallon and compressor energy costs are $1.93 per psi hour. The WPSS is restricted to 10,000 gallons per day for snow making operations. Currently, the WPSS has one engineer and one assistant working per shift to manage snow making operations. The Director of Operations is concerned he will need additional personnel support for snowmaking, so he needs you to determine what pressure to run the compressor to minimize hourly costs. *Hint: Use, 85 314, 610 gal/hr, to verify your Mathematica code is entered correctly.* Applied MMA Lab 1 Assignment Format: 1. Briefly describe the problem you are trying to solve: 2. What known facts influence the problem: 3. Give two assumptions needed to help you solve the problem: 4. Explain how you solved the problem (use only words in this section): Course Assessment Page 2 of 3 Applied MMA Lab 1 Assignment Format: 5. State your objective function and show the math you used to solve the problem. Include any related mathematica output and include one Figure (plot) that helps reinforce your conclusion: 6. Would your solution change if the compressor was not restricted to a set psi? Explain: 7. What pressure should the Director of Operations choose, and how much will it cost per hour? 8. How many hours per day can they operate the new snow making system and what is the total cost of operation in a day? Course Assessment Page 3 of 3 ...
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