Assignment #3 (80 Points) – COSC 5390 –Dr. Leonard Brown Due: April 4, 2013 (atthe beginning of class) Problem Description Write a java program that will implement the Simplex algorithm discussed in class that will solve a systemof equationsin the following form. Maximize Z = c 1x 1 +…+ c nx n Subjectto a 11x 1 +…+ a 1nx n ≤ b1 a 21x 1 +…+ a 2nx n ≤ b2 … a m1x 1 +…+ a mnx n ≤ b m and xi ≥ 0 fori=1,…,n Input The input programwill be a systemof inequalities augmented with slack variablesso thatitisin a formsuitable forthe “table”method. So, ifthe goal wasto solve the following system: Maximize Z = 3×1 + 5×2 x 1 ≤ 4 2×2 ≤ 12 3×1 + 2×2 ≤ 18 xj ≥ 0,forj = 1, 2 Then the input to the program will be represented by the following system of equations (with the slack variablesincluded). Z – 3x 1 – 5x 2 = 0 x 1 + x 3 = 4 2×2 + x 4 = 12 3×1 + 2×2 + x 5 = 18 More specifically,the inputto the programwould be the following lines oftext 1 -3 -5 0 0 0 0 0 1 0 1 0 0 4 0 0 2 0 1 0 12 0 3 2 0 0 1 18 Which comesfromthe shaded area in the following table: Basic Var Eq Z x 1 x 2 x 3 x 4 x 5 Right Side Z 0 1 ‐3 ‐5 0 0 0 0 x 3 1 0 1 0 1 0 0 4 x 4 2 0 0 2 0 1 0 12 x 5 3 0 3 2 0 0 1 18
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