April 2007 - M = 2 4 1 3 1 4 2 I-M-1 = 1 3 4 7 2 1 6 3 1 8 1 4(B X = MX D ⇐⇒ X = I-M-1 D(C The output is $81 billion from agriculture $49

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MATH-208. ANSWERS TO THE FINAL APRIL 2007 Problem 1 : (A) Demand: p ( q ) = 2 q + 2 (B) Supply: p ( q ) = - q + 11 (C) The equilibrium price is 8 for the demand = supply q = 3 (in hundreds) Problem 2 : (A) x = 12 (B) x = - 9 or x = 6 (C) x = 27 3 (D) x = 14 (E) x = 5 Problem 3 : (A) n = 130 payments, i = 0 . 075 52 , PMT = $ 209.98 per week (B) n = 60 payments, i = 0 . 075 24 , PMT = $ 455.37 twice a month (C) Total payments under (B) - Total payments under (A) = 60 · 455 . 37 - 130 · 209 . 98 = 24 . 80 Problem 4 : Loan = PV = 2,000,000, r = 0 . 065 , m = 52 , i = r m = 0 . 00125 , n = 520 payments (A) PMT = $5 , 232 . 95 per week (B) $741,258.40 (C) n = 371 . 53 ' 372 weekly payments (D) Total payments in (A) - Total payments in (C) = 372 · 6732 . 95 - 520 · 5232 . 95 . 98 = 216 . 60 Problem 5 : x = # of hoppers with capacity 3,000; y = # of of hoppers with capacity 4,500; z = # of of hoppers with capacity 6,000 The possible solutions are: { x = 0 ,y = 8 ,z = 12 } ; { x = 1 ,y = 6 ,z = 13 } ; { x = 2 ,y = 4 ,z = 14 } ; { x = 3 ,y = 2 ,z = 15 } ; { x = 4 ,y = 0 ,z = 16 } (B) The minimum cost of $5,700 is attained at { x=0, y=8, z=12 } . Problem 6 : A - 1 = - 0 . 9 5 - 0 . 1 0 . 8 - 4 0 . 2 0 . 1 0 - 0 . 1 Problem 7 :
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Unformatted text preview: M = . 2 . 4 . 1 . 3 . 1 . 4 . 2 ( I-M )-1 = 1 . 3 . 4 . 7 . 2 1 . 6 . 3 . 1 . 8 1 . 4 (B) X = MX + D ⇐⇒ X = ( I-M )-1 · D (C) The output is: $81 billion from agriculture, $49 billion from energy, and $62 billion from manufacturing. Problem 8 : Bounded region with the corner points: (6 , 0) , (10 , 0) , (6 , 12) , (0 , 15) , (0 , 4) The minimum of -600 is attained at (0, 15) and the maximum of 200 is attained at (10, 0). Problem 9 : (A) C 15 , 3 · C 20 , 1 = ( 15 3 ) · ( 20 1 ) = 9 , 100 (B) C 15 , 2 · C 20 , 2 = ( 15 2 ) · ( 20 2 ) = 19 , 950 (C) C 15 , 4 = ( 15 4 ) = 1 , 365 (D) C 35 , 4 = ( 35 4 ) = 52 , 360 (E) sum of (A) and (C) = 10 , 465. Problem 10 : (A) ( 74 10 ) ( 80 10 ) = 0 . 4363 (B) 1-. 4363 = 0 . 5637 1...
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This note was uploaded on 04/13/2011 for the course MATH 209 taught by Professor Chekhov during the Winter '07 term at Concordia Canada.

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