ACCA PM · Chapter 6 · Question 4 of 10
Omega Co makes products X and Y. Contribution is $40 per unit of X and $50 per unit of Y. Constraints are: Labour: 2x + 4y <= 4,000 hours Machine: 3x + 2y <= 3,600 hours Demand for X: x <= 1,000 units where x and y are the units of X and Y produced. What is the optimal production plan?
Test yourself: pick an answer
Reveal answer & explanation
Correct answer: C) 800 units of X and 600 units of Y
Explanation
Solving the binding labour and machine constraints simultaneously: from 2x + 4y = 4,000, x = 2,000 - 2y; substituting into 3x + 2y = 3,600 gives 6,000 - 4y = 3,600, so y = 600 and x = 800. Contribution at the vertices is: (0, 1,000) $50,000; (800, 600) $62,000; (1,000, 300) $55,000; (1,000, 0) $40,000. The optimum is 800 X and 600 Y. The combination 1,000 X and 500 Y breaches the machine constraint.
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