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CMA Final · Strategic Cost Management · Linear Programming

In a maximisation LP for Bharat Tools, the constraint x + 2y ≤ 10 for machine hours is converted to standard form for the simplex method. Which treatment is correct?

A less-than-or-equal-to constraint is converted by adding a non-negative slack variable, giving x + 2y + s = 10. The slack represents unused machine hours. Surplus and artificial variables belong to greater-than-or-equal-to constraints, so they are not required here.

  1. ASubtract a surplus variable and add an artificial variable
  2. BAdd a slack variable: x + 2y + s = 10, s ≥ 0Correct
  3. CAdd a slack variable: x + 2y - s = 10, s ≥ 0
  4. DAdd an artificial variable only, with a profit coefficient of zero

Explanation

A 'less than or equal to' constraint is converted to an equation by adding a non-negative slack variable representing unused machine hours. Surplus and artificial variables are used for 'greater than or equal to' or equality constraints. Subtracting the slack, as in the third option, would be wrong in sign.

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