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Industrial Engineering Operations Research - Operations Research I

# Industrial Engineering Operations Research - Operations Research I

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Fall 2009 IEOR 160 Industrial Engineering & Operations Research September 8, 2009 Page 1 of 3 HOMEWORK 1 SOLUTIONS Chapter 12.1 1. lim h 0 3 h + h 2 h = lim h 0 3 + h = 3. 3. (a) - xe x + e x (b) 2 x ( x 2 +1) 2 x 3 ( x 2 +1) 2 (c) 3 e 3 x (d) - 6 (3 x +2) 3 (e) 3 x 4. ∂f ∂x 1 = 2 x 1 e x 2 ∂f ∂x 2 = x 2 1 e x 2 2 f ∂x 2 1 = 2 e x 2 2 f ∂x 1 ∂x 2 = 2 f ∂x 2 ∂x 1 = 2 x 1 e x 2 2 f ∂x 2 2 = x 2 1 e x 2 5. ln(1 + h ) = h - h 2 2 + 2 p 3 3! for p [1 , 1 + h ]. Chapter 12.2 1. (a) Let S = soap opera ads and F = football ads. Then we wish to min z = 50 S + 100 F s.t. 5 S + 17 F 40 20 S + 7 F 60 S 0 ,F 0 (b) Since doubling S does not double the contribution of S to each constraint, we are violating the proportionality assumption. Additivity is not violated. (c) This accounts for the fact that an extra soap opera ad yields a benefit which is a de- creasing function of the number of football ads. This accounts for the fact that we may not want to double count people who see both types of ads.

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Industrial Engineering Operations Research - Operations Research I

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