Let's break down the problem step by step: --- ### **Given Data** #### **Figure 1: Parts Moved Between Work Centers (Flow Matrix)** | | A | B | C | D | |---|-----|-----|-----|-----| | A | 0 | 325 | 420 | 600 | | B | 0 | 0 | 200 | 50 | | C | 0 | 0 | 0 | 750 | | D | 0 | 0 | 0 | 0 | #### **Figure 2: Existing Layout** A – 30’ – B – 30’ – C – 30’ – D --- ## **a) Calculate the cumulative "load × distance" or "movement cost" for the existing layout** ### **Step 1: Find Distances Between Centers** - A to B: 30' - A to C: 30' + 30' = 60' - A to D: 30' + 30' + 30' = 90' - B to C: 30' - B to D: 30' + 30' = 60' - C to D: 30' ### **Step 2: Find Flows (from matrix) and Calculate Movement Cost** #### **From A:** - A to B: 325 × 30 = 9,750 - A to C: 420 × 60 = 25,200 - A to D: 600 × 90 = 54,000 #### **From B:** - B to C: 200 × 30 = 6,000 - B to D: 50 × 60 = 3,000 #### **From C:** - C to D: 750 × 30 = 22,500 #### **From D:** - No outgoing flow. #### **Sum All Movement Costs:** 9,750 + 25,200 + 54,000 + 6,000 + 3,000 + 22,500 = **120,450** --- ### **Final Answer for (a):** **120,450 feet** --- ### **b) Determine which center should go between A and D to minimize the movement cost** #### **Look for Highest Flows** - Highest flow: C to D (750 moves) - Second highest: A to D (600 moves) - Next: A to C (420 moves) - Next: A to B (325 moves) - Next: B to C (200 moves) - Next: B to D (50 moves) #### **What should be between A and D?** To minimize the cost, the work center with the HIGHEST flow with either A or D should be placed between them, ideally aligning those with high interactivity closer together. #### **Look at the fixed positions**: > Positions: [___] --30'-- [A] --30'-- [___] --30'-- [D] We need to choose between B and C for the middle spot. - C to D: 750 moves (largest single flow), so **C should be next to D**. - A to C: 420 moves, so **C should also be closer to A** than B. - So, **C should be between A and D**. --- **Fill in the blank:** > In the improved layout, the work center that should be located between A and D is **C**. --- ### **Cumulative Distance in Improved Layout** **New layout: B - A - C - D** (since A and D are fixed and C should be between them, B is left for the other end). **Distances:** - A to B: 30' - A to C: 30' - A to D: 60' - B to C: 60' - B to D: 90' - C to D: 30' **Now, recalculate movement cost:** #### **From A:** - A to B: 325 × 30 = 9,750 - A to C: 420 × 30 = 12,600 - A to D: 600 × 60 = 36,000 #### **From B:** - B to C: 200 × 60 = 12,000 - B to D: 50 × 90 = 4,500 #### **From C:** - C to D: 750 × 30 = 22,500 **Total for new layout:** 9,750 + 12,600 + 36,000 + 12,000 + 4,500 + 22,500 = **97,350** --- ## **Summary of Answers** ### **a) Existing layout cumulative movement cost:** **120,450 feet** ### **b) Work center to locate between A and D:** **C** ### **Cumulative movement cost for improved layout:** **97,350 feet** --- If you need any part of the explanation clarified, let me know!