## Final Exam

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## Final Exam

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- Pages:
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- School:
- Towson University
- Course:
- Math 111 - Finite Mathematics

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Final Exam Math 111 May 17 2005 Name All questions are worth an equal number of points All work is to be done on the blank paper provided At the end of the exam please hand in this sheet together with all of your work 1 Calculation 1 Graph the feasible set for the system of inequalities 3x 4y x y 3x y x 0 y 8 9 21 0 Find the maximum of f x 3x 11y on this feasible set 2 Write the system of linear equations 9x 7y 6 5x 4y 11 in the form AX B for matrices A X and B identify A X and B Find A 1 and use it to solve the system 3 Use the simplex method to maximize the function 10x y subject to the constraints x 2y 10 3x 4y 6 x y 0 4 Use the simplex method to minimize the function 3x 2y subject to the constraints x y 10 x y 15 x y 0 5 Evaluate 6 6 6 6 6 6 6 a 0 1 2 3 4 5 6 32 32 32 32 32 b 2 3 4 5 32 6 Suppose that an experiment consists of tossing a coin four times and observing the sequence of heads and tails Order matters a What is the sample space S b Let E1 be the event that two or more heads appear What is E1 c Let E2 be the event that two or more tails appear What is E2 d What is E1 E2 Give both the elements as well as a description in words 2 Comprehension 7 What is the geometric definition of slope 8 What are the elementary row operations 9 When are you allowed to mutiply two matrices Give an example of a pair of matrices A and B so that the product AB is defined calculate it and so that the product BA is not defined 10 Define the following terms experiment outcome sample space event 3 Application 11 For tax purposes businesses must keep track of the current value of their assets A common mathematical model is to assume that the current value y is related to the age x of the asset by a linear equation A moving company buys a 40 foot van with a useful life of 5 years After x months of use the value y of the van is estimated by the linear equation y 25 000 400x a Sketch the graph of this linear equation b What is the value of the van after 5 years c What economic

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