- Sterling Manufacturing faces a bottleneck in its finishing department, which has 480 hours of capacity per month. The company produces two products with the following characteristics: Product A requires 3 finishing hours per unit with $90 contribution margin; Product B requires 8 finishing hours per unit with $180 contribution margin. If Sterling has firm commitments to deliver 80 units of Product A monthly, what production plan maximizes contribution margin for the remaining capacity?
Answer: Use remaining 240 hours to produce 80 additional units of Product A for total contribution margin of $14,400
When facing bottleneck constraints, you need to maximize contribution margin per unit of the constraining resource. This is a classic theory of constraints problem where limited finishing department capacity drives the optimization decision.
First, calculate contribution margin per finishing hour for each product: Product A generates 3 hours$90=$30 per hour, while Product B generates 8 hours$180=$22.50 per hour. Since Product A provides higher contribution margin per constraining resource hour, you should prioritize it.
With the 80-unit commitment requiring 80×3=240 hours, you have 480−240=240 remaining hours. Using all remaining capacity for Product A allows production of 3240=80 additional units, generating 80×$90=$7,200 incremental contribution margin. Total contribution margin becomes (160×$90)=$14,400.
Answer A correctly calculates the incremental contribution margin of $7,200 but incorrectly states this as the total. Answer B wastes the superior resource utilization of Product A by producing only 30 units of Product B for $5,400 incremental margin. Answer C splits capacity inefficiently, producing some of the lower-margin-per-hour Product B instead of maximizing Product A production.
Remember: In bottleneck situations, always rank products by contribution margin per unit of the constraining resource, not by absolute contribution margin per unit. The highest absolute margin doesn't matter if it ties up too much of your limited resource. - Which resource is the binding constraint, and what is the optimal product mix to maximize contribution margin?
Answer: Skilled labor is binding; produce 400 units of Fabric A only
When facing constrained resource problems, you need to identify which constraint is most limiting and then determine the optimal product mix by comparing contribution margins per unit of the constraining resource.
First, let's identify the binding constraint by calculating the maximum units possible under each constraint. For machine hours: Fabric A allows 600 units (1,200÷2), Fabric B allows 400 units (1,200÷3), and Fabric C allows 1,200 units (1,200÷1). For skilled labor hours: Fabric A allows 800 units (800÷1), Fabric B allows 400 units (800÷2), and Fabric C allows 400 units (800÷2).
Since skilled labor creates tighter restrictions for Fabrics B and C, skilled labor is the binding constraint. Next, calculate contribution margin per skilled labor hour: Fabric A earns $40 per hour ($40÷1), Fabric B earns $37.50 per hour ($75÷2), and Fabric C earns $17.50 per hour ($35÷2). Fabric A provides the highest return per constrained resource unit.
With 800 skilled labor hours available and Fabric A requiring 1 hour per unit, you can produce 400 units of Fabric A, generating $16,000 in contribution margin.
Answer A incorrectly focuses on total contribution per unit rather than per constrained resource. Answer B wrongly identifies machine hours as binding and ignores the skilled labor constraint. Answer D correctly identifies 400 units of Fabric A but incorrectly states machine hours as the constraint.
Remember: always identify the true bottleneck first, then maximize contribution margin per unit of that constraining resource, not per product unit.
- If Zenith wants to maximize total contribution margin, what is the optimal monthly production mix?
Answer: 800 units of Alpha, 0 units of Beta, 0 units of Gamma
To maximize contribution margin under a bottleneck constraint, calculate contribution margin per hour of the constraint resource. Alpha: $45 ÷ 3 hours = $15/hour; Beta: $52 ÷ 4 hours = $13/hour; Gamma: $28 ÷ 2 hours = $14/hour. Alpha has the highest contribution margin per constraint hour, so produce Alpha exclusively: 2,400 hours ÷ 3 hours per unit = 800 units. Choice B focuses only on total contribution margin per unit (Beta highest), Choice C uses the shortest processing time without considering contribution margin, and Choice D attempts an equal allocation without optimizing the constraint.
- Vertex Electronics has 1,800 hours of assembly time available monthly. The company produces two products: Standard units requiring 3 assembly hours with $75 contribution margin, and Deluxe units requiring 9 assembly hours with $180 contribution margin. Current firm orders are 200 Standard and 100 Deluxe units. If Vertex can modify the Deluxe product design to reduce assembly time to 6 hours while maintaining the $180 contribution margin, how would this change affect the optimal use of remaining capacity?
Answer: Switch to producing Deluxe units with remaining capacity since the design change makes Deluxe more profitable per hour
Current firm orders consume: Standard (200 × 3) + Deluxe (100 × 9) = 600 + 900 = 1,500 hours. Remaining: 1,800 - 1,500 = 300 hours. Before design change: Standard = $75 ÷ 3 = $25/hour; Deluxe = $180 ÷ 9 = $20/hour. Standard is optimal for remaining capacity. After design change: Standard = $25/hour; Deluxe = $180 ÷ 6 = $30/hour. Deluxe becomes optimal with higher contribution per hour. Also, firm orders change to: (200 × 3) + (100 × 6) = 600 + 600 = 1,200 hours, leaving 600 hours remaining. Choice A ignores the improvement in Deluxe contribution per hour. Choice C incorrectly states they become equal. Choice D suggests arbitrary mixing rather than optimization.
- What combination of products should Crystal Electronics produce to maximize monthly contribution margin, and what is the maximum achievable contribution margin?
Answer: 1,920 Premium tablets only, generating $268,800 contribution margin
Calculate contribution margin per hour of bottleneck time. Standard: $80 ÷ (1/20) = $1,600 per hour. Premium: $140 ÷ (1/12) = $1,680 per hour. Premium has higher contribution margin per constraint hour, so produce Premium exclusively: 160 hours × 12 tablets/hour = 1,920 tablets × $140 = $268,800. Choice A uses only Standard tablets (suboptimal). Choice C attempts a 50-50 split. Choice D uses a 5:1 ratio based on processing time differences rather than contribution margin optimization.
- After meeting the standing orders, what should Delta do with the remaining capacity to maximize contribution margin?
Answer: Produce additional Alpha units since Alpha has the highest contribution margin per constraint hour at $40
When you encounter a bottleneck constraint problem, the key is maximizing contribution margin per unit of the constraining resource—not per product unit. You need to calculate contribution margin per constraint hour for each product to determine the most profitable use of limited capacity.
First, let's calculate the contribution margin per hour for each product: Alpha generates 5 hours$200=$40 per hour, Beta generates 8 hours$280=$35 per hour, and Gamma generates 4 hours$140=$35 per hour.
Next, determine remaining capacity after fulfilling standing orders: Alpha uses 100×5=500 hours, Beta uses 50×8=400 hours, leaving 2,000−500−400=1,100 hours available.
Since Alpha provides the highest contribution margin per constraint hour at $40, Delta should produce additional Alpha units with the remaining capacity. Answer C correctly identifies this optimal strategy.
Answer A incorrectly focuses on production efficiency (fitting more units into available hours) rather than profitability per hour. Answer B makes the common error of comparing absolute contribution margins per unit instead of contribution per constraint hour—Beta's $280 per unit is less valuable when you consider it takes 8 hours to earn it. Answer D mentions Alpha but gives incorrect reasoning about time requirements rather than the proper constraint analysis.
Remember: in constraint problems, always calculate contribution margin per unit of the limiting factor. The product with the highest margin per constraint unit should receive priority for any remaining capacity.
