# hw7 - Homework 7 Deterministic Optimization ISYE 6669...

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Unformatted text preview: Homework 7 Deterministic Optimization ISYE 6669 12.2.1 Part A Let S = soap opera ads and F = football ads. Then we wish to minimize: z = 50 S + 100 F s.t. 5 √ S + 17 √ F ≥ 40 20 √ S + 7 √ F ≥ 60 S ≥ ,F ≥ Part B Since double S does not double the contribution of S to each constraint, we are violating the propor- tionality assumption. Additivity is not violated. 12.2.11 MAX =- 1 . 4 T + . 4 TEMP- 2 . 2 T 2- 3 . 2 TEMP 2- 4 . 9 T * TEMP s.t. T = TIME- 90 10 TEMP = TEMPER- 150 5 TIME ≥ 60 TIME ≤ 120 TEMPER ≥ 100 TEMPER ≤ 200 Objective Function Value = 2.257349 T = -2.631225; TEMP = 2.077030; TIME = 63.687750; TEMPER = 160.385150 1 12.3.3 f ′′ ( x ) = 2 x − 3 > for x > . Thus f ( x ) is convex on S . 12.3.4 f ′′ ( x ) = a ( a- 1) x a − 2 ≤ so f ( x ) is concave on S . 12.3.6 H = parenleftbigg 6 x 1 3 3 2 parenrightbigg For x 1 < , the first principal minor is 6 x 1 < and for x 1 > the first principal minor is 6 x 1 > . Thus f ( x 1 ,x 2 ) cannot be convex or concave. 12.3.9 H = - 2 . 5 . 5- 2- 4 First order principal minors are -2, -2, -4 which are all strictly less than zero. Second order principal minors are all strictly greater than zero. det parenleftbigg- 2 . 5 . 5- 2 parenrightbigg = 3 . 75 det parenleftbigg- 2- 4 parenrightbigg = 8 det parenleftbigg- 2- 4 parenrightbigg = 8 Expanding by Row 3 we find the third order principal minor =...
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hw7 - Homework 7 Deterministic Optimization ISYE 6669...

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