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HW7 Solutions - 29 2 50 f x x x =-= giving x = 25 lbs as...

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OSCM 230 Homework 07 H O M E W O R K # 7 N O N L I N E A R P R O G R A M M I N G 6-38. Let X 1 = number of four-cylinder engines to produce, and X 2 = number of six-cylinder engines to produce. Objective: Maximize profit = X 1 (1,800 - 50X 1 ) + X 2 (2,400 - 70X 2 ) = 1,800X 1 –50X 1 2 + 2,400X 2 - 70X 2 2 Subject to: 100X 1 + 130X 2 5,000 hours X 1 , X 2 0 Solution: See file P6-38.XLS. X 1 X 2 Solution value 18.00 17.14 Profit $36,771.43 6-40. There are three decision variables corresponding to the percent of the portfolio dedicated to Alpha, Beta, and Gamma. Objective: Minimize variance = 3A 2 + 2B 2 + 2G 2 + 2AB - 1.1AG - 0.7BG Subject to six constraints: total investment, minimum return, maximum Alpha, maximum Beta, maximum Gamma, and non-negativity. Solution: See file P6-40.XLS. A B G Solution value 0.21 0.33 0.46 Variance 0.70 H O M E W O R K # 7 S O L U T I O N S ( E X T R A P R O B L E M S ) N O N L I N E A R P R O G R A M M I N G 1. Page 1 of 4
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OSCM 230 Homework 07 2. Total cost per pound is given by ( 29 ( 29 3 2 2 50 750 50 750 f x x x x x x x = - + = - + . Taking the first derivative and setting it to zero yields
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Unformatted text preview: ( 29 * * 2 50 f x x x =-= , giving x * = 25 lbs. as the quantity that minimizes total cost per lb. This quantity produces a total cost of $3125. 3. Page 2 of 4 OSCM 230 Homework 07 where units of purchased 1, 2 units of purchased and shipped in cars 1, 2, respectively units of purchased 1, 1 units from car 1 to produce and , respectively 2, 2 units from car 2 to produc A A B B B C C TX TY X Y TX TY = = = = = e and , respectively 1, 2 % sulfur in cars 1, 2, respectively X Y TS TS = The NLP is Max 9 15 6 16 1 2 10 X Y A B B C +--+ ( 29 -s.t. X ≤ 100 Y ≤ 200 1 1 1 2 2 2 1 2 1 2 3 1 1 1 2 2 2 2 1 1 2 2 2.5 1 1 2 2 1.5 A B TX TY B C TX TY X TX TX Y TY TY A B TS A B B C TS B C TX TS TX TS X TY TS TY TS Y + = + + = + = + = + + = + + = + + + all var’s nonnegative Page 3 of 4 OSCM 230 Homework 07 Page 4 of 4...
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HW7 Solutions - 29 2 50 f x x x =-= giving x = 25 lbs as...

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