Subjects algebra

Production Cost 3D5Ea5

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Production Cost 3D5Ea5


1. **State the problem:** We have four products A, B, C, and D with different production costs and quantities. The total number of items produced is 173,340. We want to find the percentage of total production cost for each product to adjust the pie chart accordingly. 2. **Define variables and relationships:** Let the number of Product A items be $x$. - Product B items: $1.5x$ - Product C items: $2 \times$ Product B $= 2 \times 1.5x = 3x$ - Product D items: $3 \times$ Product B $= 3 \times 1.5x = 4.5x$ 3. **Total items equation:** $$x + 1.5x + 3x + 4.5x = 173,340$$ $$10x = 173,340$$ $$x = \frac{173,340}{10} = 17,334$$ 4. **Calculate quantities:** - Product A: $17,334$ - Product B: $1.5 \times 17,334 = 26,001$ - Product C: $3 \times 17,334 = 52,002$ - Product D: $4.5 \times 17,334 = 77,503$ 5. **Calculate total production cost for each product:** - Product A cost: $7.50 \times 17,334 = 130,005$ - Product B cost: $5.40 \times 26,001 = 140,405.4$ - Product C cost: $3.30 \times 52,002 = 171,606.6$ - Product D cost: $1.00 \times 77,503 = 77,503$ 6. **Calculate total cost:** $$130,005 + 140,405.4 + 171,606.6 + 77,503 = 519,520$$ 7. **Calculate percentage of total cost for each product:** - Product A: $$\frac{130,005}{519,520} \times 100 \approx 25.02\%$$ - Product B: $$\frac{140,405.4}{519,520} \times 100 \approx 27.03\%$$ - Product C: $$\frac{171,606.6}{519,520} \times 100 \approx 33.04\%$$ - Product D: $$\frac{77,503}{519,520} \times 100 \approx 14.91\%$$ **Final answer:** The pie chart should be adjusted to approximately: - Product A: 25.02% - Product B: 27.03% - Product C: 33.04% - Product D: 14.91% These percentages represent the share of total production cost for each product.