Sure! Let's solve each part step by step. I'll first transcribe the text for clarity, then show the calculations and final answers. --- ### **Transcribed Problem:** **Daleman Company produces helmets (Model H42).** - Setup time: 2 days - Production rate: 750 units/day - Expected annual demand: 36,000 units - Lead time: 8 days **Customer order:** 12,000 helmets, but the stipulation is that the helmets be delivered within one week (7 days) after order is placed. --- ### **Required:** #### **1. Calculate the optimal batch size for Model H42 using the EOQ model.** **EOQ (Economic Order Quantity) for production =** \[ Q^* = \sqrt{\frac{2DS}{H} \cdot \frac{P}{P-d}} \] Where: - \( D = \) annual demand = 36,000 units - \( S = \) setup cost (not given, but not needed for just batch size since only time and rates matter in this context) - \( H = \) holding cost per unit per year (not given explicitly) - \( P = \) production rate = 750 units/day - \( d = \) demand rate = 36,000 units/year = 100 units/day So: \[ Q^* = \sqrt{\frac{2DS}{H} \cdot \frac{P}{P-d}} \] But since setup cost and holding cost are not given, let's use the formula for a production run: \[ \text{Batch size} = \frac{\text{Daily demand} \times \text{Setup time}}{1 - \frac{\text{Daily demand}}{\text{Production rate}}} \] But typically, EOQ for production is: \[ \text{Optimal Lot Size} = \sqrt{\frac{2DS}{H} \times \frac{P}{P-d}} \] Since S and H are not given, let's focus on the process time: #### **2. Was Bateman’s response to the customer right? Would a lot size be time-indicated to produce the number of units wanted by the customer?** **Production Rate** = 750 units/day **Units needed** = 12,000 **Days to produce** = \( \frac{12,000}{750} = 16 \) days **Required delivery time** = 7 days **Conclusion:** No, it's not possible to produce 12,000 units in 7 days at 750 units/day. #### **3. Do you agree or disagree with the manager's grumbling about Bateman's inventory policy?** "Last week the order because we didn’t have sufficient inventory. We try to keep more units in inventory to deal with unexpected orders like these.” **Agree/Disagree:** Agree. **Reason:** If you don’t keep buffer (safety stock), you can’t meet large, sudden orders. #### **4. How much additional inventory would have been needed to meet the customer’s requirement?** **Customer wants** = 12,000 units **in 7 days** **Current inventory:** Assume none, since they couldn’t fulfill. **Additional inventory needed = Order quantity = 12,000 units** #### **5. Is it common for the account demand to occur from just a few, very large orders during the year, as Daleman had to carry more inventory?** **Yes** — For lumpy or irregular demand, companies keep higher safety stock. #### **6. Lead time reduction:** If setup time is reduced to 0.5 day and total lead time to 5 days, what is the batch size now? (Round to nearest whole number.) **Production rate** = 750 units/day **Total time to meet order** = 5 days **Units produced in 5 days = 750 × 5 = 3,750 units** But they need 12,000 units. So, If setup time is reduced to 0.5 day, and total time is 5 days: \[ \text{Units produced in 5 days} = 750 \times 5 = 3,750 \text{ units} \] But if the batch size is asked for the *production run*: \[ \text{Batch size} = \text{Production rate} \times \text{Production time} \] (But for EOQ, more details would be needed.) --- ### **Summary Table of Answers:** #### **1. Calculate the optimal batch size for Model H42 using the EOQ model.** - **Optimal batch size:** N/A (not enough data to calculate EOQ without setup or holding cost) #### **2. Was Bateman’s response correct?** - **No.** It is not possible to produce 12,000 units in 7 days at 750 units/day. #### **3. Do you agree with the manager’s grumbling?** - **Agree.** Safety stock is needed for unexpected large orders. #### **4. How much additional inventory would have been needed?** - **12,000 units.** #### **5. Is it common for this type of order pattern, and does it require more inventory?** - **Yes.** #### **6. If setup time is reduced to 0.5 day and lead time to 5 days, what is the batch size?** - **3,750 units.** --- **If you want more detail or have the setup/holding costs, I can calculate actual EOQ!**