1. **Problem Statement:** Determine the optimal production plan for A & B Ltd given constraints on grinding labor hours and compare financial outcomes between budgeted and optimal plans. 2. **Data Summary:** - Anker: - Direct Materials: 10,000 CFA - Grinding: 5 per hr, 7 hrs/unit - Finishing: 7.5 per hr, 15 hrs/unit - Selling Price: 206,500 CFA - Budgeted Production: 1,200 units - Max Sales: 1,500 units - Barker: - Direct Materials: 30,000 CFA - Grinding: 5 per hr, 5 hrs/unit - Finishing: 7.5 per hr, 9 hrs/unit - Selling Price: 168,000 CFA - Budgeted Production: 600 units - Max Sales: 800 units 3. **Step 1: Calculate contribution per unit for each product.** Contribution per unit = Selling Price - Variable Costs (Materials + Labour) - Labour costs grinding per unit: - Anker: $5 \times 7 = 35$ - Barker: $5 \times 5 = 25$ - Labour costs finishing per unit: - Anker: $7.5 \times 15 = 112.5$ - Barker: $7.5 \times 9 = 67.5$ - Total variable cost per unit: - Anker: $10 + 35 + 112.5 = 157.5$ - Barker: $30 + 25 + 67.5 = 122.5$ - Contribution per unit: - Anker: $206.5 - 157.5 = 49$ - Barker: $168 - 122.5 = 45.5$ 4. **Step 2: Calculate contribution per hour of grinding (the bottleneck).** Grinding hours per unit: - Anker: 7 hrs - Barker: 5 hrs Contribution per grinding hour: - Anker: $\frac{49}{7} = 7$ - Barker: $\frac{45.5}{5} = 9.1$ Since Barker has higher contribution per grinding hour, prioritize Barker. 5. **Step 3: Calculate total grinding hours available.** Budgeted production grinding hours: - Anker: $1,200 \times 7 = 8,400$ - Barker: $600 \times 5 = 3,000$ Total grinding hours available = $8,400 + 3,000 = 11,400$ hours 6. **Step 4: Determine optimal production plan under grinding constraint.** Maximize contribution by producing Barker first up to max sales: - Barker max units = 800 - Grinding hours for Barker max = $800 \times 5 = 4,000$ Remaining grinding hours for Anker: - $11,400 - 4,000 = 7,400$ Anker units producible: - $\frac{7,400}{7} = 1,057$ units (rounded down) 7. **Step 5: Calculate total contribution for budgeted and optimal plans.** - Budgeted plan contribution: - Anker: $1,200 \times 49 = 58,800$ - Barker: $600 \times 45.5 = 27,300$ - Total: $58,800 + 27,300 = 86,100$ - Optimal plan contribution: - Barker: $800 \times 45.5 = 36,400$ - Anker: $1,057 \times 49 = 51,793$ - Total: $36,400 + 51,793 = 88,193$ 8. **Step 6: Advice** The optimal plan yields higher contribution (88,193) than the budgeted plan (86,100). A & B Ltd should prioritize producing Barker to max sales first, then use remaining grinding hours for Anker to maximize profit.