1. **State the problem:** Determine the optimal production plan for A & B Ltd given constraints on grinding labor and compare financial outcomes between budgeted and optimal plans. 2. **Identify key data:** - Direct materials per unit: Anker = 10, Barker = 30 (000CFA) - Grinding labor hours per unit: Anker = 7, Barker = 5 - Finishing labor hours per unit: Anker = 15, Barker = 9 - Selling price per unit: Anker = 206.5, Barker = 168 (thousands CFA) - Budgeted production: Anker = 1200 units, Barker = 600 units - Maximum sales: Anker = 1500 units, Barker = 800 units - Grinding labor is limited to budgeted production hours. 3. **Calculate contribution per unit:** Contribution = Selling price - Direct materials - Direct labor (grinding + finishing) Calculate direct labor cost per unit: - Anker grinding: $5 \times 7 = 35$ - Anker finishing: $7.5 \times 15 = 112.5$ - Barker grinding: $5 \times 5 = 25$ - Barker finishing: $7.5 \times 9 = 67.5$ Total direct labor per unit: - Anker: $35 + 112.5 = 147.5$ - Barker: $25 + 67.5 = 92.5$ Contribution per unit: - Anker: $206.5 - 10 - 147.5 = 49$ - Barker: $168 - 30 - 92.5 = 45.5$ 4. **Calculate grinding labor hours available:** Budgeted grinding hours = $(1200 \times 7) + (600 \times 5) = 8400 + 3000 = 11400$ hours 5. **Determine contribution per grinding hour:** - Anker: $\frac{49}{7} = 7$ per hour - Barker: $\frac{45.5}{5} = 9.1$ per hour Since Barker has higher contribution per grinding hour, prioritize Barker. 6. **Optimal production plan:** - Maximize Barker production to max sales: 800 units - Grinding hours used by Barker: $800 \times 5 = 4000$ - Remaining grinding hours: $11400 - 4000 = 7400$ - Anker production with remaining hours: $\frac{7400}{7} \approx 1057$ units 7. **Calculate total contribution for budgeted and optimal plans:** - Budgeted: - Anker: $1200 \times 49 = 58800$ - Barker: $600 \times 45.5 = 27300$ - Total: $58800 + 27300 = 86100$ - Optimal: - Barker: $800 \times 45.5 = 36400$ - Anker: $1057 \times 49 = 51793$ - Total: $36400 + 51793 = 88193$ 8. **Advice:** Optimal plan increases contribution by $88193 - 86100 = 2093$ (000CFA). A & B Ltd should adopt the optimal plan prioritizing Barker production due to higher contribution per grinding hour.