Question

3) How can you use simplex algorithm to find the roots of the following equations. Explain clearly No need to solve simplex alporithm.) x,+3x2 +1-

Answer 1

Given 3 x_1 + a x_2 - 1 = 0 3 x_1 + 3 x_2 + 1 = 0 Taking standard equations a_1 x_1 + b_1 x_2 + c_1 = 0 a_2 x_2 + b_2 x_2 + c_2 using cross multiplication to find the roots x/b_1 c_2 - b_2 c_1 = x_2/c_1 a_2 - c_2 a_1 = 1/a_1 b_2 - a_2 b_1 therefore x_1 = b_1 c_2 - b_2 c_1/a_1 b_2 - a_2 b_1 and x_2 = c_1 a_2 - c_2 a_1/a_1 b_2 - a_2 b_1 given 3 x_1 + 9 x_2 - 1 = 0 3 x_1 + 3 x_2 + 1 = 0 using algorithm of cross multiplication x_1/(9) (1) - (-1) (3) = x_2/(-1) (3) - (1) (3) = 1/(3) (3) - (9) (3) implies x_1/9 + 3 = x_2 /-3 - 3 = 1/9 - 27 implies x_1/12 = x_2/-6 = 1/-12 implies x_1 = 12/18 = -2/3 and x_2 = -6/-18 = 1/3 are the roots of the equations