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CMA Final · Strategic Cost Management · Linear Programming

Sundaram Foods maximises Z = 3x + 2y subject to x + y ≤ 4, x + 3y ≤ 6, x ≤ 3, x, y ≥ 0. Using the optimal solution, which statement is correct?

The optimum is Z = 11 at x = 3, y = 1, where x ≤ 3, x + y ≤ 4 and x + 3y ≤ 6 are all exactly satisfied, so all three bind. Other corners give only 9 or 4.

  1. AOptimal Z is 10, with the constraint x + 3y ≤ 6 fully used
  2. BOptimal Z is 11, with all three constraints binding
  3. COptimal Z is 9, and x ≤ 3 has slack of 1
  4. DOptimal Z is 10, with x ≤ 3 and x + y ≤ 4 binding and x + 3y ≤ 6 having slackCorrect

Explanation

Corners: (3,0)=9; (3,1)=11? Check feasibility: x+3y=3+3=6 ok, x+y=4 ok, so (3,1) is feasible and Z=9+2=11. Hence all three constraints bind at (3,1) and Z=11. Other corners: (0,2)=4, (3,0)=9. The correct statement is Z=11 with all constraints binding.

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