Consider the following math program (MP): Minimize Z = (x1 - 7)^2 + (x^2 - 6)^2

Question

Consider the following math program (MP): Minimize Z = (x1 - 7)^2 + (x^2 - 6)^2 subject to x1^2 + x2^2 lessthanorequalto 81 2x1^2 + 3 x2^2 lessthanorequalto 144 x1 greaterthanorequalto 2 x2 greaterthanorequalto 3 x1, x2 greaterthanorequalto 0 (a) Graph the non-linear functions (components) and demonstrate that the MP is separable. I. Determine if the objective function is convex or concave and WHY? II. Determine if constraint 1 is convex or concave and WHY? III. Determine if constraint 2 is convex or concave and WHY? (b) Linearize the MP by the Method of Segment Variables and solve resulting model using LINDO. (c) Linearize the MP by the Method of Segment weights and solve resulting model using LINDO. (d) Compare the results you obtained from parts (b) and (c) by tabulating your results for Z, X1, and X2.

Explanation / Answer

z=(x1 - 7)2 + ( X2 - 6)2 = x21 + x22 + 85 - 14x1 -12x2   

   becouse x21+x22 < 81

; 81+85 - 28 - 36=102 if x1>2 & x2 >3 so z will be

z <102

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