1. **Problem Statement:** Calculate all material variances for materials A and B using the given data and prove the equation $$\text{MCV} = \text{MPV} + \text{MUV}$$. 2. **Given Data:** - Standard cost for 100 units: - Material A: 100 kg @ 10 - Material B: 1500 kg @ 8 - Actual usage and cost: - Material A: 90 kg @ 9 - Material B: 1600 kg @ 10 3. **Formulas:** - Material Cost Variance (MCV): $$\text{MCV} = (\text{SQ} \times \text{SP}) - (\text{AQ} \times \text{AP})$$ - Material Price Variance (MPV): $$\text{MPV} = (\text{SP} - \text{AP}) \times \text{AQ}$$ - Material Usage Variance (MUV): $$\text{MUV} = (\text{SQ} - \text{AQ}) \times \text{SP}$$ - Material Yield Variance (MYV): $$\text{MYV} = (\text{SQ} - \text{AQ}) \times \text{ASP}$$ 4. **Calculate Average Standard Price (ASP):** $$\text{ASP} = \frac{(100 \times 10) + (1500 \times 8)}{100 + 1500} = \frac{1000 + 12000}{1600} = \frac{13000}{1600} = 8.125$$ 5. **Calculate Standard Quantity (SQ) for actual production:** - Total actual quantity used = 90 + 1600 = 1690 kg - Material A SQ: $$100 \times \frac{1690}{1600} = 105.625 \approx 106 \text{ kg}$$ - Material B SQ: $$1500 \times \frac{1690}{1600} = 1584.375 \approx 1584 \text{ kg}$$ 6. **Calculate Material Cost Variance (MCV):** - Material A: $$ (106 \times 10) - (90 \times 9) = 1060 - 810 = 250 \text{ (Favorable)}$$ - Material B: $$ (1584 \times 8) - (1600 \times 10) = 12672 - 16000 = -3328 \text{ (Adverse)}$$ - Total MCV: $$250 - 3328 = -3078 \text{ (Adverse)}$$ 7. **Calculate Material Price Variance (MPV):** - Material A: $$ (10 - 9) \times 90 = 1 \times 90 = 90 \text{ (Favorable)}$$ - Material B: $$ (8 - 10) \times 1600 = -2 \times 1600 = -3200 \text{ (Adverse)}$$ - Total MPV: $$90 - 3200 = -3110 \text{ (Adverse)}$$ 8. **Calculate Material Usage Variance (MUV):** - Material A: $$ (106 - 90) \times 10 = 16 \times 10 = 160 \text{ (Adverse)}$$ - Material B: $$ (1584 - 1600) \times 8 = -16 \times 8 = -128 \text{ (Favorable)}$$ - Total MUV: $$160 - 128 = 32 \text{ (Adverse)}$$ 9. **Verify the equation:** $$\text{MCV} = \text{MPV} + \text{MUV}$$ $$-3078 = -3110 + 32$$ $$-3078 = -3078$$ This confirms the equation holds true. **Final Answer:** - Material Cost Variance (MCV) = -3078 (Adverse) - Material Price Variance (MPV) = -3110 (Adverse) - Material Usage Variance (MUV) = 32 (Adverse) - Equation $$\text{MCV} = \text{MPV} + \text{MUV}$$ is verified.