# Finite math exam

An economy has 3 goods: honey (good 1), roses (good 2), and tealeaves (good 3). The technology matrix A is given below. Also given are (I-A) and (I-A)-l . If there is a demand for 100 units of honey, 90 units of roses, and 40 units of tealeaves, how many units of roses need to be produced? . 95 c. 670 d. 460 e. 44 g. 358 h. 348 I. 32 k. 13 4. The economy of Pointless has two goods: rubber balls (good 1) and urns (good 2). The production of each ball requires 0. 7 balls and 0. 4 urns. The production of each urn requires 0. 2 balls and 0. 4 urns. If there is a production schedule for 300 rubber balls and 240 urns, what is the demand vector? B. D. H. J. None of the above drinks an extra 5 ounces of water that day. When she rows for 25 minutes, she drinks an extra 9 ounces of water that day.

It is known that the amount of extra eater she consumes in a day is a linear function of her time on the rowing machine on that day. How long does she row if Jaime drinks 20 ounces of extra water? C. 17. 5 d. 75 e. 52. 5 f. 77. 5 g. 21 h. 25 I. 60 j. 21. 6 k. 35. 1 6. Recall that I is the identity matrix. Find the (2, 2) entry of the inverse of B. I. 0. 5 m. Not this one o. -1/3 B has no inverse q. R. None of the above h. -11 I. 13 j. -15 k. 15 8. When a matrix has no inverse, the matrix is said to be singular. The matrix below is singular for one and only one value of k.

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What is that value of k? . Cannot be determined 9. Caroline and Orrin are very competitive dart players (and good at Markova chains). Every week they play two games of darts with each other, and one of three things happens: Caroline wins both games (state 1), Orrin wins both games (state 2), or they split the games (state 3). Orrin win both games is 0. 70, and the probability that they split is two times the probability that Caroline wins both games. If Orrin wins both games one week, then the following week the probability that Caroline wins both games is 0. 5, and the arability that Orrin wins both games is four times the probability that they split the games. If they split the games one week, the following week they do not split the games, and there is an equal probability that Caroline wins both games and that Orrin wins both games. Which of the following is the transition matrix for this Markova chain? 10. A squirrel can be found in any of 4 statesвЂ”Alabama(1), Colorado (2), Delaware (3), and Exhaustion (4). It is known that this is a Markova process with the transition matrix given below.