All work must be shown clearly. Please mark your final answers. Use appropriate units and complete sentences. You may work with others on this portion of the exam. Good luck. 1) A couple has up to $40,000 to invest in mutual funds. Their broker recommends investing in two funds based on their average annual return for 5 years ending on December 31, 2009: The Templeton Global Bond fund yielding 6.7% and the Franklin International Small Cap Growth fund yielding 8.9%. After some consideration the couple decides to invest at most $15,000 in the Franklin International Small Cap Growth fund and at least $18,000 in the Templeton Global Bond Fund. What should the broker recommend if the couple wants to maximize the return on their investment? Graphical representation of the solution is required for this problem. 2) Put this matrix in reduced row echelon form and solve the system. Correct format of the answer is critical here: 1 2 -1 0 1 0 1 4 1 2 0 1 -2 3 0 6 -6 3) 2x + y + z X - Y - Z 3x +y +22 = 6 =-3 = 7 Solve the system of equations either by using pair-wise elimination, substitution or Gaussian elimination. Clearly show your steps to receive full credit. Present the solution as the point of intersection (ordered triple). 4) For American roulette there are only two possibilities: earnings of $1 or loss of $1. These occur with probabilities and respectively. What is the expected value for American Roulette? (European Roulette is different.) SHOW YOUR WORK. 18 38 20 38 5) An oil drilling company may only bid for one job, out of three possible contracts. If oil is discovered in the North Sea, which has a 33% chance of happening, the company would profit Euro 3.75 million, and it would cost the company Euro 600,000 to get set-up. If oil was discovered in the Barents Sea, which has a 46% chance of happening, the company would profit Euro 2.85 million and it would cost Euro 345,000 to get the equipment set up. Which job do you recommend they bid on? Complete sentence answers are required. SHOW ALL WORK. 6) Sheila wants to invest an amount every 3 months so that she will have $32,000 six years from today, to buy a new car. The account pays 6.45% compounded quarterly. How much should she deposit each quarter to have $32,000 after 6 years? Appropriate answer format is crucial. 7) A Broadway theater has 1500 seats, divided into Orchestra, Main and Balcony seating. Orchestra sells for $80 per ticket, $65 for Main and $45 for Balcony. If all the seats are sold the gross revenue is $96,450. If all Main and Balcony seats are sold, but only half the Orchestra seats, then Revenue drops to $78,450. How many seats are there of each kind? (Complete sentence answers required, with appropriate units). SHOW YOUR WORK. 7) A Broadway theater has 1500 seats, divided into Orchestra, Main and Balcony seating. Orchestra sells for $80 per ticket, $65 for Main and $45 for Balcony. If all the seats are sold the gross revenue is $96,450. If all Main and Balcony seats are sold, but only half the Orchestra seats, then Revenue drops to $78,450. How many seats are there of each kind? (Complete sentence answers required, with appropriate units). SHOW YOUR WORK. 8) How many ways can you choose 3 flavors, at Baskin Robbins (which offer 31 flavors), for a banana split? All work must be shown clearly. Please mark your final answers. Use appropriate units and complete sentences. You may work with others on this portion of the exam. Good luck. 1) A couple has up to $40,000 to invest in mutual funds. Their broker recommends investing in two funds based on their average annual return for 5 years ending on December 31, 2009: The Templeton Global Bond fund yielding 6.7% and the Franklin International Small Cap Growth fund yielding 8.9%. After some consideration the couple decides to invest at most $15,000 in the Franklin International Small Cap Growth fund and at least $18,000 in the Templeton Global Bond Fund. What should the broker recommend if the couple wants to maximize the return on their investment? Graphical representation of the solution is required for this problem. 2) Put this matrix in reduced row echelon form and solve the system. Correct format of the answer is critical here: 1 2 -1 0 1 0 1 4 1 2 0 1 -2 3 0 6 -6 3) 2x + y + z X - Y - Z 3x +y +22 = 6 =-3 = 7 Solve the system of equations either by using pair-wise elimination, substitution or Gaussian elimination. Clearly show your steps to receive full credit. Present the solution as the point of intersection (ordered triple). 4) For American roulette there are only two possibilities: earnings of $1 or loss of $1. These occur with probabilities and respectively. What is the expected value for American Roulette? (European Roulette is different.) SHOW YOUR WORK. 18 38 20 38 5) An oil drilling company may only bid for one job, out of three possible contracts. If oil is discovered in the North Sea, which has a 33% chance of happening, the company would profit Euro 3.75 million, and it would cost the company Euro 600,000 to get set-up. If oil was discovered in the Barents Sea, which has a 46% chance of happening, the company would profit Euro 2.85 million and it would cost Euro 345,000 to get the equipment set up. Which job do you recommend they bid on? Complete sentence answers are required. SHOW ALL WORK. 6) Sheila wants to invest an amount every 3 months so that she will have $32,000 six years from today, to buy a new car. The account pays 6.45% compounded quarterly. How much should she deposit each quarter to have $32,000 after 6 years? Appropriate answer format is crucial. 7) A Broadway theater has 1500 seats, divided into Orchestra, Main and Balcony seating. Orchestra sells for $80 per ticket, $65 for Main and $45 for Balcony. If all the seats are sold the gross revenue is $96,450. If all Main and Balcony seats are sold, but only half the Orchestra seats, then Revenue drops to $78,450. How many seats are there of each kind? (Complete sentence answers required, with appropriate units). SHOW YOUR WORK. 7) A Broadway theater has 1500 seats, divided into Orchestra, Main and Balcony seating. Orchestra sells for $80 per ticket, $65 for Main and $45 for Balcony. If all the seats are sold the gross revenue is $96,450. If all Main and Balcony seats are sold, but only half the Orchestra seats, then Revenue drops to $78,450. How many seats are there of each kind? (Complete sentence answers required, with appropriate units). SHOW YOUR WORK. 8) How many ways can you choose 3 flavors, at Baskin Robbins (which offer 31 flavors), for a banana split