1. **State the problem:** Calculate single-factor productivity for rubber and OCLV Carbon, multi-factor productivity in dollars for last year, and the expected multi-factor productivity for the coming year with a 12% increase. 2. **Formulas and rules:** - Single-factor productivity (SFP) = Output / Input (in physical units, not dollars) - Multi-factor productivity (MFP) = Output (revenue) / Total input cost - Total input cost = sum of (input amount × cost per unit) - Increase by 12% means multiply last year's MFP by 1.12 3. **Given data:** - Output (units produced) = 1970 bikes - Average selling price per bike = 7200 - Inputs and costs: - Labor Hours: 11800 hours at 23.25 each - OCLV Carbon: 1100 sq ft at 14.22 each - Rubber: 2825 pounds at 3.65 each - Paint: 470 gallons at 22.70 each - Energy: 11620280 kWh at 0.14 each 4. **Calculate single-factor productivity for rubber:** $$\text{SFP}_{rubber} = \frac{\text{Output units}}{\text{Rubber input}} = \frac{1970}{2825} \approx 0.6979$$ 5. **Calculate single-factor productivity for OCLV Carbon:** $$\text{SFP}_{OCLV} = \frac{1970}{1100} \approx 1.7909$$ 6. **Calculate total input cost:** $$\text{Total cost} = (11800 \times 23.25) + (1100 \times 14.22) + (2825 \times 3.65) + (470 \times 22.70) + (11620280 \times 0.14)$$ Calculate each term: - Labor: $274350$ - OCLV Carbon: $15642$ - Rubber: $10311.25$ - Paint: $10669$ - Energy: $1626839.2$ Sum: $$274350 + 15642 + 10311.25 + 10669 + 1626839.2 = 1937811.45$$ 7. **Calculate total output revenue:** $$1970 \times 7200 = 14184000$$ 8. **Calculate multi-factor productivity:** $$\text{MFP} = \frac{14184000}{1937811.45} \approx 7.32$$ 9. **Calculate next year's expected MFP with 12% increase:** $$7.32 \times 1.12 = 8.20$$ **Final answers:** - Single-factor productivity (rubber): 0.6979 - Single-factor productivity (OCLV Carbon): 1.7909 - Multi-factor productivity (last year): 7.32 - Multi-factor productivity (next year): 8.20