Answered: Problem Set A (1) The table below shows…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Transcribed Image Text:12:23 PM O O ECON1003 Undergraduate Program Problem Set A (1) The table below shows the calories, fat, and carbohydrates per ounce for three brands of cereal, and the total amount of calories, fat, and carbohydrates required for a special diet. Calories Fat Carbohydrates Cereal Brand x 50 22 Cereal Brand Y 108 0.1 25.5 Cereal Brand Z 127 5.5 18 Total Required 393 5.7 91 (i) Using the information in the table above, write a system of three equations. (ii) Write a system in matrix form Ar=b. (ii) Using the Cramer's Rule or Inverse Method, find the amount of each brand of cereal that will give the level of nutrition required. (2) For the function f(x) =-x' -24x+19 6) Determine the turning points and the values of the function at each turning point. (ii) Determine the point of inflection, any exist. (iii) What is the range of value over which the function is strictly increasing (iv) What is the range of values over which the function is concave upwards. (3) A production manager determines that t months after production on a new product begins, 17 +13 (2r +1) the number of units produced will be N thousand, where N(1) = (i) What would be the level of production 5 months into operations. (ii) What would be the level of production be in the long run. THE UNIVERSITY OF THE WEST INDIES OPEN CAMPUS Page 19 of 36 ECONIO03 Mahematies for the Social Sciences 1-Course laformmation. Academic Year 2021/2022, Semester 1 Problem Set B (1) If the total cost of a firm is C(x) =1.5x' -5x + 20.x +5. Find the marginal cost (in dollars) when 25 units are produced and sold. (2) The number q of roller blades a firm is willing to sell per week at a price of $p is given by q = 60p+25 +300 for 20s ps100. (i) Find dg dp (ii) Find the amount supplied when the price is $56. (ii) Find the instantaneous rate of change of supply with respect to price when the price is $56. (3) (i) A broken pipe at an oil rig off the east coast of Trinidad produces a circular oil slick that is S meters thick at a distance x meters from the break. It difficult to measure the thickness of the slick directly at the source owing to excess turbulence, but for x>0 they know that SCx) -- 2 '3 I+x+2x

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