(a) Convert the inequality constraints in the following data to equations by adding slack variables or subtracting surplus variables and express the equations in matrix form,

(b) Determine the number of variables that must be set equal to zero to find a basic solution and read the first basic solution from the matrix.

(a) For “less than or equal to” inequalities, add slack variables.

Expressed in matrix form,

(b) With v = 5 and n = 3, 5 – 3 = 2 variables must be set equal to zero. Setting y1 = y2 = 0 and multiplying, the initial basic solution is s1 = −36, s2 = −84, and s3 = −16. Since this initial basic solution contains negative values, it is not feasible.

Transcribed Image Text:

Maximize = 7x1 +21x2 subject to 5x12x240 3x1 +12x260- 4x18x248 x1, x2 0