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This 0 page Class Notes was uploaded by Douglas Conroy PhD on Sunday November 1, 2015. The Class Notes belongs to MATH at Indiana University taught by Andrew Dabrowski in Fall. Since its upload, it has received 8 views. For similar materials see /class/233402/math-indiana-university in Mathematics (M) at Indiana University.
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Date Created: 11/01/15
Finite Chapter 5 DNE is used here for does not exist 1 3 points Find the slope of the line 2x 43 1 2 3 points Find the slope of the line 33 7 3 8 points Sketch the graph of the line 21 33 9 Indicate the x and y intercepts 4 4 points Write the equation of the line through the point 3 1 that is parallel to the line 21 33 7 5 3 points each The following augmented matrices are in reduced form If the corresponding system of equations in x y and 2 has no solutions say so If it has a unique solution give it If it has in nitely many solutions identify the free variables and give formulas for the other vari ablels in terms of the free ones 1 2 0 3 a 0 0 1 4 0 0 0 0 1 0 0 3 b 0 1 0 2 0 0 0 1 1 3 2 5 c 0 0 0 0 0 0 0 0 6 8 points Put the following augmented matrix in row reduced form 2 4 1 0 3 5 1 1 4 7 1 2 7 8 points The evil math AI Iksworbad Werdna is concocting a diabolical exam for the algebra course he s teaching The exam will consist entirely of long and extremely confusing story problems Iksworbad likes 3 different types of story problems materials and products problems MampP for short combination and permuation problems CampP for short and problems with several variables SV for short But composing really dif cult story problems is hard work In fact in writing a single good M scP Iksworbad uses up 1 whole pencil and 6 sheets of paper and requires 2 hours of work A CampP requires 1 pencil and 4 sheets of paper and 1 hours An SV requires 1 pencils 11 sheets 00 C 1 O 1 1 1 M 9quot r 3 points Solve the equation of paper and 3 hours Assuming Iksworbad has only a dozen pencils and 100 sheets of paper and must have the exam in to the math department Copying Goddess in 36 hours how many problems of each type can he make Set up an augmented matrix which would be used to determine how many of each type of problem to write in order to use up all the resources Iksworbad has available You need not row reduce the matrix 8 points The evil math AI Iksworbad Werdna has made at least one scienti c discovery since he started grad school He has established a linear relationship between the number of story problems he puts on an algebra exam and the number of anonymous death threats left on his answering machine When he puts 5 story problems on an exam he gets 5 death threats when he puts 9 story problems on an exam he gets 11 death threats He is planning to put 15 story problems on his next exam and needs to know whether he needs a longer cassette for his answering machine to hold all the messages the exam will generate How many death threats can Iksworbad expect to receive as a result of this exam Chapter 6 3 points each De ne matrices A B C and D as follows 1 1 1 0 2 A gB 3 02 0 11 1 0 1 2 1 2 1 0 Compute the following showing work If the expression is undefined just say so a AB 30 1 21 BC c BOA d CBA x 23 3 4 points Give the matrix equation form of the system 1 33 z y 22 4 X P QX for X You may assume the existence of any inverse matrix you need 8 points Use a matrix inverse to solve the following 3 systems 1 y 0 x y x3y2 x3y0 8 points Huge Hughie s Hoagies sells sandwiches Hughie makes all the day s hoagies potato salad and iced tea himself every morning Hughie has a big appetite and cooking makes him very hungry While making 10 hoagies he eats half a hoagy half a cup of potato salad and 1 glass of iced tea While making 10 cups of potato salad he eats i of a hoagy half a cup of potato salad and half a glass of iced tea While making a gallon of iced tea 16 glasses he eats a cup of potato salad and 2 glasses of iced tea Give the technology matrix for the Huge Hughie s Hoagies xy 2 x3y 4 8 points Suppose that A 396 398 is a technolo Ty matrix Use Leontief theory for the followinr 2 1 5 s 0 1 G3 a Find D if the current production schedule is 70 units of the rst product and 30 units of the second b Find the production schedule X required to meet an external demand for 40 units of the first product and 50 units of the second 39 8 points Compute the inverse of the following matrix Show your work 0 1 1 1 1 1 1 2 1 Chapter 7 Formulate the following word problem as a linear programming problem De ne your variables specify the objective function and goal max or min and give all the constraints Do not attempt to solve it Max Machines assembles PCs from parts and sells the complete units They make three different systems a multimedia system which is sold at a pro t of 1000 an internet system sold at a pro t of 700 and a budget system sold at a pro t of 400 The multimedia system requires a processor chip a large monitor and accessories worth 600 The internet system requires a processor a small monitor and 300 worth of accessories The budget system requires a processor a small monitor and 100 worth of accessories In addition the company has 1000 man hours of labor available every month for assembly Each mulitmedia system requires 3 hours for assembly each internet system requires 2 hours for assembly and each budget system requires 1 hour for assmebly Every month Intel is able to supply up to 100 processor chips 10000 dollars is available each month to spend on accessories Another supplier is able to provide up to 100 small and up to 50 large monitors Assuming Mac Machines sells all the systems it builds how many systems of each type should they make Graph the system of inequalities Do not find the corner points just shade the feasible set Be sure to label the lines with the corresponding equations 120 320 xy22 2x yZ 3 335 Find the maximum and minimum of the objective function 21 33 on the given shade feasible set Be aware that I have not made the diagram particularly accurate yiaxis Chapter 1 Practice Exam 1 2 QC 0 E33 3 points each Let A B and C be sets and suppose that nA 4 nB 6 nC 8 also suppose that A and B are disjoint and that nB 1 C 4 Find the sizes of the following sets 1 AXBUC iLMnme iMUme 3 points each Let U be the universe of D117 students Let S be the students who study hard for the first exam let E be the students who are too exhausted from their other classes to study for math let B be the students who find math too boring to able to study it without falling into a coma and let R be the students who did poorly on the rst exam and have to retake it Translate the following set expressions into pure English ie don t use any set theory jargon like intersection complement etc Note that some are full sentences and some are just noun phrases ie no verb 1 S CR irwumcy iii SCR iv E B S R 6 points Draw a Venn diagram to represent the expression A U B 1 C 10 points A box contains 2 pennies 2 nickels and a dime An experiment consists of drawing coins one at a time in succession without replacement noting the denomination each time until the dime is drawn Make the tree diagram for this experiment How large is the sample space 6 points A box contains a marble a ball bearing and a ping pong ball a bowl contains red white and blue marbles An experiment consists of drawing two objects in succession without replacement from the box then drawing two balls in succession with replacement from the bowl on each of the 4 draws noting the object drawn How large is the sample space 15 points A math instructor has 17 calculators in his desk l39ine of them are graphing calculators 8 are programmable and another 7 offer RPN reverse Polish notation entry format Of those with RPlV 4 do graphing and 3 are prgrammable Only one calculator has all three features 2 calculators are just basic four bangers with none of the special features How many programmable calculators does the instructor have that also do graphing