Let's solve the **aggregate planning** problem step by step for **part a: "Produce exactly to meet demand, vary workforce."** I'll explain each step and provide the final answer for this part. --- ### **Given Data Summary** - **Demand** (monthly): as per table. - **No. of working days:** as per table. - **Material Cost:** ₹120/unit - **Inventory holding cost:** ₹10/unit/month - **Stockout cost:** ₹150/unit/month - **Subcontracting cost:** ₹420/unit - **Hiring cost:** ₹500/worker - **Firing cost:** ₹1500/worker - **Labor hours/unit:** 5 - **Regular wages:** ₹100/hr - **Overtime wages:** ₹150/hr (not needed for part a) - **Initial Inventory:** 200 units - **Initial Workforce:** 15 --- ## **Step 1: Calculate Monthly Production Requirement** ### **A. Net Production Requirement Each Month** Net Requirement = Demand - Beginning Inventory (for Jan) For each next month: Net Requirement = Demand - Ending Inventory (previous month) But since we are producing **exactly to meet demand**, we want **ending inventory = 0** each month (except Jan, which starts with 200 units). Hence, for Jan: - Production needed = Demand - Beginning Inventory = 600 - 200 = **400 units** For Feb onward, since ending inventory is 0: - Production needed = Demand --- ## **Step 2: Calculate No. of Workers Needed** ### **B. Productivity per Worker per Month** Each worker works 8 hours/day × No. of working days = Total hours/month Each unit requires 5 hours to produce. **Units produced per worker/month = (8 × No. working days) / 5** Let's calculate for each month: | Month | Working Days | Worker Hours | Units/Worker | |-----------|-------------|-------------|--------------| | January | 26 | 208 | 208/5 = 41.6 | | February | 22 | 176 | 176/5 = 35.2 | | March | 26 | 208 | 41.6 | | April | 25 | 200 | 40 | | May | 26 | 208 | 41.6 | | June | 25 | 200 | 40 | | July | 26 | 208 | 41.6 | | August | 26 | 208 | 41.6 | | September | 25 | 200 | 40 | | October | 26 | 208 | 41.6 | | November | 25 | 200 | 40 | | December | 26 | 208 | 41.6 | --- ### **C. Number of Workers Required Each Month** **No. of Workers = Production Required / Units per Worker** #### **January** - Production = 400 units - Units/worker = 41.6 - Required Workers = 400 / 41.6 = **9.62 → 10 workers** (round up) #### **February** - Production = 500 units (demand) - Units/worker = 35.2 - Required Workers = 500 / 35.2 = **14.2 → 15 workers** #### **March** - Production = 600 units - Units/worker = 41.6 - Required Workers = 600 / 41.6 = **14.42 → 15 workers** #### **April** - Production = 500 units - Units/worker = 40 - Required Workers = 500 / 40 = **12.5 → 13 workers** #### **May** - Production = 600 units - Units/worker = 41.6 - Required Workers = 600 / 41.6 = **14.42 → 15 workers** #### **June** - Production = 800 units - Units/worker = 40 - Required Workers = 800 / 40 = **20 workers** #### **July** - Production = 700 units - Units/worker = 41.6 - Required Workers = 700 / 41.6 = **16.83 → 17 workers** #### **August** - Production = 700 units - Units/worker = 41.6 - Required Workers = 700 / 41.6 = **16.83 → 17 workers** #### **September** - Production = 700 units - Units/worker = 40 - Required Workers = 700 / 40 = **17.5 → 18 workers** #### **October** - Production = 650 units - Units/worker = 41.6 - Required Workers = 650 / 41.6 = **15.62 → 16 workers** #### **November** - Production = 800 units - Units/worker = 40 - Required Workers = 800 / 40 = **20 workers** #### **December** - Production = 600 units - Units/worker = 41.6 - Required Workers = 600 / 41.6 = **14.42 → 15 workers** --- ## **Step 3: Calculate Hiring and Firing** Starting workforce = 15. | Month | Required Workers | Hired (+) / Fired (-) | Workforce at Month End | |------------|-----------------|-----------------------|-----------------------| | January | 10 | -5 (fire) | 10 | | February | 15 | +5 (hire) | 15 | | March | 15 | 0 | 15 | | April | 13 | -2 (fire) | 13 | | May | 15 | +2 (hire) | 15 | | June | 20 | +5 (hire) | 20 | | July | 17 | -3 (fire) | 17 | | August | 17 | 0 | 17 | | September | 18 | +1 (hire) | 18 | | October | 16 | -2 (fire) | 16 | | November | 20 | +4 (hire) | 20 | | December | 15 | -5 (fire) | 15 | --- ## **Step 4: Calculate Total Cost for Each Month** ### **Components:** - **Material Cost:** ₹120 × Production - **Labor Cost:** No. of workers × working days × 8 × ₹100 - **Hiring/Firing Cost:** As per above - **Inventory Cost:** Only in January (for 200 units) Let's break down **January** as an example: #### **January:** - **Production:** 400 units - **Material cost:** 400 × ₹120 = ₹48,000 - **Labor cost:** 10 workers × 26 days × 8 hr × ₹100 = 10 × 208 × ₹100 = ₹208,000 - **Hiring cost:** 0 - **Firing cost:** 5 × ₹1500 = ₹7,500 - **Inventory holding:** 200 units × ₹10 = ₹2,000 **Total Cost Jan = 48,000 + 208,000 + 7,500 + 2,000 = ₹265,500** --- ### **You should repeat this calculation for each month using the above method.** --- ## **Summary Table** | Month | Prod. | Req. Workers | Hired | Fired | Material | Labor | Hiring | Firing | Inventory | Total Cost | |-----------|-------|--------------|-------|-------|----------|----------|--------|--------|-----------|-------------| | January | 400 | 10 | 0 | 5 | 48,000 | 208,000 | 0 | 7,500 | 2,000 | 265,500 | | February | 500 | 15 | 5 | 0 | 60,000 | 264,000 | 2,500 | 0 | 0 | 326,500 | | March | 600 | 15 | 0 | 0 | 72,000 | 312,000 | 0 | 0 | 0 | 384,000 | | April | 500 | 13 | 0 | 2 | 60,000 | 260,000 | 0 | 3,000 | 0 | 323,000 | | May | 600 | 15 | 2 | 0 | 72,000 | 312,000 | 1,000 | 0 | 0 | 385,000 | | June | 800 | 20 | 5 | 0 | 96,000 | 400,000 | 2,500 | 0 | 0 | 498,500 | | July | 700 | 17 | 0 | 3 | 84,000 | 353,600 | 0 | 4,500 | 0 | 442,100 | | August | 700 | 17 | 0 | 0 | 84,000 | 353,600 | 0 | 0 | 0 | 437,600 | | September | 700 | 18 | 1 | 0 | 84,000 | 360,000 | 500 | 0 | 0 | 444,500 | | October | 650 | 16 | 0 | 2 | 78,000 | 332,800 | 0 | 3,000 | 0 | 413,800 | | November | 800 | 20 | 4 | 0 | 96,000 | 400,000 | 2,000 | 0 | 0 | 498,000 | | December | 600 | 15 | 0 | 5 | 72,000 | 312,000 | 0 | 7,500 | 0 | 391,500 | --- ## **Final Answer (for (a))** **You should produce exactly to meet demand each month, varying the workforce accordingly. The total cost for each month is shown in the table above.** --- ### **If you need the full calculations for part b or c, let me know!**