Optimal Product Mix

Ideal vs Real World

• Ideal World:

  • Unlimited resources
  • Equal contribution margins
  • All customer orders accepted

• Real World:

  • Resources are limited
  • Products require different resource quantities
  • Contribution margins vary
  • We must optimize the product mix for profit

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Example Scenario

Machine Constraint

• Total Machine Time Available: 600 hours/month
• Cooling Time: 4 hours/day → not available for production
• Products: X and Y

Product	Machine Hours per Unit	Contribution per Unit	Contribution per Machine Hour
X	2 hours	₹100	₹50 (100 ÷ 2)
Y	3 hours	₹135	₹45 (135 ÷ 3)

➡️ Product X is preferred (higher contribution per hour)

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Constraints

Constraint Type	Product X	Product Y
Minimum Units	50 units	40 units
Maximum Units	200 units	No limit
Machine Time Req.	100 hours	120 hours

• Time used for minimum production = 220 hours
• Time left for allocation = 600 - 220 = 380 hours

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Optimal Allocation Strategy

1. Prioritize Product X due to higher efficiency
   • Max additional units of X = 150 (200 max - 50 min)
   • Time needed = 150 × 2 = 300 hours
2. Remaining time = 380 - 300 = 80 hours
   • Product Y uses 3 hours per unit → can produce ≈ 27 units

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Final Product Mix

Product	Base Qty	Extra Qty	Total Units	Total Time Used
Product X	50	150	200	400 hours
Product Y	40	27	67	201 hours
Total Time Used				~601 hours (rounding effect)

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Key Learning: Contribution Per Unit of Constraint

• When machine hours are limited → compute ₹ per machine hour
• When labour hours are limited → compute ₹ per labour hour
• When raw materials are limited → compute ₹ per unit of raw material

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📌 Conclusion

• Use marginal costing + constraints to guide production decisions
• Always respect minimum/maximum limits
• Prioritize products that give highest contribution per constraint
• This is a basic form of linear programming, useful in:
  • Capacity planning
  • Short-term profit maximization
  • Decision-making under limited resources

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