Homework 1 Solutions
Homework 1b
Part 1: Inventory, Throughput Rate, and Flow Time
• Short-Term:
o Throughput Rate (R): 200 cars/week
o Flow Time (T): 0.5 weeks
o Inventory (I): 100 cars
• Long-Term:
o Throughput Rate (R): 100 cars/week
o Flow Time (T): 2 weeks
o Inventory (I): 200 cars
• Cleaning:
o Throughput Rate (R): 240 cars/week
o Flow Time (T): 0.4167 weeks (which is approximately 2.92 days)
o Inventory (I): 100 cars
• Repair:
o Throughput Rate (R): 60 cars/week
o Flow Time (T): 2 weeks
o Inventory (I): 120 cars
Part 2: Profit Calculation with Current Demand
• Revenue:
o Short-term: $15,000 (200 cars * $150 * 0.5 week)
o Long-term: $24,000 (100 cars * $120 * 2 weeks)
• Costs:
o Cleaning Cost: $1,200 (240 cars * $5)
o Repair Cost: $9,000 (60 cars * $150)
o Depreciation: $20,800 (Total inventory * $40 per week)
• Profit:
o Profit = Revenue - Costs
o Profit = $15,000 + $24,000 - $1,200 - $9,000 - $20,800 = $8,000
Part 3: Profit Calculation with Increased Short-Term Demand
• Short-Term:
o Throughput Rate (R): 400 cars/week
o Flow Time (T): 0.5 weeks
o Inventory (I): 200 cars
• Cleaning:
o Throughput Rate (R): 400 cars/week
o Flow Time (T): 0.4167 weeks (approximately 2.92 days)
o Inventory (I): 166.67 cars
• Repair:
o Throughput Rate (R): 100 cars/week
o Flow Time (T): 2 weeks
o Inventory (I): 200 cars
• Revenue:
o Short-term: $30,000 (400 cars * $150 * 0.5 week)
o Long-term: $24,000 (100 cars * $120 * 2 weeks)
• Costs:
o Cleaning Cost: $2,000 (400 cars * $5)
o Repair Cost: $15,000 (100 cars * $150)
o Depreciation: $30,667 (Total inventory * $40 per week)
• Profit:
o Profit = Revenue - Costs
o Profit = $30,000 + $24,000 - $2,000 - $15,000 - $30,667 = $6,333.33
