Answer all questions

7. Complete one of the word problems below. Remember to show your work and answer in complete sentences. You can do one more for extra credit, but mark this one clearly. Work on the back of the page if necessary. (20 points) a. Among all pairs of number (x, y) such that 2x + y = 16, find the pair for which the sum of squares x2 + y is minimum. b. A small cruising ship that can hold up to 60 people provides 3-day excursions to groups of 38 or more. If the group contains 38 people, each person pays $74. The cost per person for all members of the party is reduced by $1 for each person in excess of 38. Find the size of the group that maximizes the income for the owners of the ship. c. At the Olympic opening ceremony, a flaming arrow is fired upward with an initial velocity of 96 ft/sec from a platform 40 feet high. What is the maximum height attained by the arrow? [Recall: h = -2gt2 + vot + ho, where g = 32 ft/sec2 = 9.8 m/sec2]