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MATH114 Lecture 21: Slides - Week 12 - Tuesday - Annotated.pdf

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4 Feb 2015

School

University of Alberta

Department

Course

Professor

Vincent Bouchard

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MATH114 Full Course Notes

MATH114 Full Course Notes

Document Summary

Last class (tuesday dec. 2nd) will be a review class. I will go through the format of the nal, and prepare a little review. I will post sample nals in the following days with a write-up of what you should expect for the nal, as i did for the midterm. A total of 3 hours; 2 hours individual part, and 1 hour group part. This week"s material was new for pretty much everyone; great! The answer is no, but the truth is that by the end of your rst year, or perhaps your second year, you will de nitely know it by heart and use it all the time. Taylor series are one of the most useful and fundamental concept in calculus Consider the function f (x) = x = 0. We are approximating f (x) at x = 0 by replacing it by its tangent line, which is the line y = l(x) such that:

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s.pearsoncmg.com/ebook/launcheText.do?values-bookID:47353: platform::1030:bookPage Go CA 114% In this application, we set up a mathematical model for deter.which ean be factored to give mining the total cost required to set up a training program. Thee we use calculus to find the time interval between training pro- grams that produces the minimum total cost. The model assumes The expression in brackets is the sum of the terms of an arithmetic that the demand for trainees is constant and that the fixed cost ofsequence discussed in most algebra texis Using formulas for arid training a batch of trainees is known. Also, it is assumed that metic sequences, we can show that the expression in brackets is people who are trained, but for whom so job is readily availahle. equal to mom-D/2, so we huve will be psid a fixed amount per month while waiting for a job to mim) The model uses the following variables: D demand for trainees per month; N= nunterofumoes per batch C fixed cost of training a batch of trainees Cvariable cost of training per trainee per month ç³.. salay pand monthly a Iraiere who has not yet as the total cos for keeping jobless trainees The total cost per betch is the sum of the training cost per hatch CmDiC, and the cost of keeping trainces without a proper job, given by equsion (X Since we anvsusme hail: batch of trainees is trained every 'n months, the total cost per mont. Zast is given by: been given a job afler training ane interval in months between successive baiches of irainees; ength of training program in months: Zm)ãtotal monthly ast of program The tal cost of training a hasch of trainees is given by Exercises c, .+ MG However, N = al, so ihal lhe total cost per batch is 1. Find Z'o a After training, personnel are given jobs al the tate of D per month ThsNDof the trainees will no gel a job the tirst month. N-2D will no get a joh the second month, and so on The N D rainees who k not get a job the tirst oets proJuce lotial costs of N- DiC hose nos gesting jobs during the second month produce cots of iN-2Co on. Since N-mD.the costs clering the irt month can be writien as 2. Solve the equation Z 0. As a practical matiet, it iND ally required that m be a positive inleger. I m does not come out to be aa integer, then ac and mÂ·the two integers claes to m, masit be choser Calculate both Zim) and onhe sualler the two provides the optimum value er 7 3. Sappose a conpuny finds that its deamand for uainees is three per llknth, that a training program reqtres l2 months. tha.he lised cost of trai ng a balch of inanees is $155xm" ta"he mrginal cost per trainee pet month is St00, and tha riinces are paid $900 per mth after training, but befte going t0 woek. Use your resuls from Exercise 2 to tiedl shilethe costs during the seondmanti-reus .. 20G, andsoon The total cost for keeping the ininees without a jab is thus ances7 How niany traces ould he in a hach? Logal Notice Privacy Policy Permissions Suppoit t Feedback 27