All questions
Question 1
Gamma Industries operates three production departments feeding a single packaging line. The packaging line can handle 1,500 units per 10-hour shift. Department A produces 180 units/hour, Department B produces 120 units/hour, and Department C produces 200 units/hour. Each department can operate independently, and products can be stored briefly before packaging. Management is evaluating whether to run departments simultaneously or sequentially to optimize packaging line utilization.
Based on the information in the passage, what constraint determines Gamma's maximum daily throughput when operating all departments simultaneously?
- Department B's production rate limits total system output to 1,200 units per 10-hour shift
- The packaging line's capacity constrains throughput to 1,500 units per 10-hour shift regardless of upstream production (correct answer)
- Combined department output of 5,000 units per shift exceeds packaging capacity, creating inventory buildup
- Department A's lower production rate compared to Department C creates an internal bottleneck within manufacturing
Explanation: When all departments run simultaneously, they produce (180+120+200) × 10 = 5,000 units per shift, but the packaging line can only handle 1,500 units. The packaging line becomes the system bottleneck. Choice A incorrectly identifies Department B as the constraint when it's actually part of combined upstream capacity. Choice C correctly notes the capacity mismatch but focuses on inventory rather than identifying the binding constraint. Choice D misunderstands that departments operate independently, not sequentially.
Question 2
Sigma Corp's assembly line has five workstations with the following cycle times: Station 1 (3 min), Station 2 (5 min), Station 3 (4 min), Station 4 (6 min), Station 5 (3 min). Management can add a parallel workstation to any single station for $200,000, reducing that station's effective cycle time by 50%. If the current contribution margin is $180 per unit and the plant operates 2,000 hours annually, which investment provides the highest return on bottleneck improvement?
- Add parallel capacity to Station 4, increasing throughput from 10 to 12 units per hour for $72,000 additional annual contribution (correct answer)
- Add parallel capacity to Station 2, increasing throughput from 10 to 20 units per hour for $360,000 additional annual contribution
- Add parallel capacity to Station 4, increasing throughput from 10 to 20 units per hour for $360,000 additional annual contribution
- Add parallel capacity to Station 1, maximizing efficiency improvement at the first production stage for optimal flow
Explanation: Station 4 (6 min) is the bottleneck, limiting throughput to 10 units/hour. Adding parallel capacity reduces Station 4's time to 3 min, but Station 2 (5 min) becomes the new bottleneck at 12 units/hour. Additional throughput: (12-10) × 2,000 × $180 = $72,000. Choice B incorrectly assumes Station 2 is the current bottleneck. Choice C miscalculates the new bottleneck after Station 4 improvement. Choice D ignores that Station 1 is not the bottleneck.
Question 3
Lambda Manufacturing's bottleneck operation currently processes 100 units per 8-hour shift with 95% quality yield, generating $50 contribution margin per good unit. Engineering proposes two alternatives: Option 1 increases processing speed to 120 units per shift while maintaining 95% yield. Option 2 maintains 100 units per shift but improves yield to 98%. Both options cost $300,000 annually. Which option better improves throughput performance?
- Option 1 generates $800 more additional daily contribution than Option 2
- Option 2 generates $150 additional daily contribution compared to $950 for Option 1
- Option 1 generates $950 additional daily contribution compared to $150 for Option 2 (correct answer)
- Both options generate equal contribution improvement since they have the same implementation cost
Explanation: When analyzing bottleneck improvements in manufacturing, you need to focus on throughput contribution—the additional profit generated by increasing the flow of good units through the constraint. The key is calculating the incremental daily contribution margin from each option.
Let's calculate the current and proposed performance. Currently, Lambda produces 100 units × 95% yield = 95 good units per shift, generating 95 × $50 = $4,750 contribution per shift.
Option 1 increases speed: 120 units × 95% yield = 114 good units per shift, generating 114 × $50 = $5,700 contribution. The additional daily contribution is $5,700 - $4,750 = $950.
Option 2 improves quality: 100 units × 98% yield = 98 good units per shift, generating 98 × $50 = $4,900 contribution. The additional daily contribution is $4,900 - $4,750 = $150.
Option 1 generates $950 additional daily contribution compared to $150 for Option 2, making C correct.
Answer A reverses the comparison incorrectly. Answer B switches which option generates which amount—a classic trap that tests whether you're carefully tracking your calculations. Answer D ignores the throughput analysis entirely by focusing only on implementation costs, missing the point that equal costs don't mean equal benefits.
For bottleneck problems, always calculate the impact on good units produced and multiply by contribution margin per unit. Don't get distracted by equal implementation costs—focus on the incremental profit each option generates through improved throughput.
Question 4
Zenith Manufacturing has three production lines feeding into a single packaging station that can process 1,200 units per hour. Line A produces 500 units/hour with a contribution margin of $8 per unit, Line B produces 400 units/hour with a contribution margin of $12 per unit, and Line C produces 450 units/hour with a contribution margin of $6 per unit. If customer demand exceeds total production capacity, which strategy will maximize throughput contribution?
- Prioritize Line B first, then Line A, then Line C based on highest contribution margin per unit
- Run all three lines simultaneously at reduced rates to maintain product mix diversity for customer satisfaction
- Prioritize Line A first, then Line C, then Line B to maximize total units processed through the bottleneck
- Prioritize Line B first, then Line A, then Line C based on contribution margin per hour of bottleneck capacity (correct answer)
Explanation: The packaging station is the bottleneck at 1,200 units/hour. To maximize throughput, prioritize based on contribution per bottleneck hour: Line B = $12 × 400 = $4,800/hour, Line A = $8 × 500 = $4,000/hour, Line C = $6 × 450 = $2,700/hour. Choice A incorrectly uses contribution per unit rather than contribution per bottleneck hour. Choice B ignores profit maximization. Choice C focuses on units rather than contribution.
Question 5
Omega Manufacturing operates a bottleneck machine 8 hours daily with setup times of 1 hour for Product A and 2 hours for Product B. Product A processes 10 units/hour after setup with $15 contribution margin per unit. Product B processes 6 units/hour after setup with $30 contribution margin per unit. If demand exists for both products and the machine can only be set up once per day, which production strategy maximizes daily throughput contribution?
- Produce Product A because it has higher processing speed and lower setup time requirements
- Produce Product B because it has higher contribution margin per unit despite longer setup time
- Produce Product A because it generates higher total daily contribution of $1,050
- Produce Product B because it generates higher total daily contribution of $1,080 (correct answer)
Explanation: Product A: (8-1) × 10 units × $15 = 70 units × $15 = $1,050. Product B: (8-2) × 6 units × $30 = 36 units × $30 = $1,080. Product B generates higher total contribution despite lower volume. Choice A ignores contribution margin differences. Choice B provides correct reasoning but doesn't show the calculation. Choice C incorrectly calculates Product A as superior.