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Profit Lumbenum Units

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Profit Lumbenum Units


1. **Problem 1: Calculate the difference in profit between 2010 and 2007 for ABC Corp sales.** Given: Salespeople earn 10% of sales as pay, business costs are 20% of sales, so profit per sale is $100\%-10\%-20\%=70\%$ of sales. 2. From the bar graph description, estimate total sales for 2007 and 2010 by summing quarterly sales (approximate from graph): - 2007 total sales $\approx 4 + 5 + 6 + 7 = 22$ million - 2010 total sales $\approx 5 + 6 + 7 + 8 = 26$ million 3. Calculate profit for each year: - Profit 2007 $= 0.7 \times 22 = 15.4$ million - Profit 2010 $= 0.7 \times 26 = 18.2$ million 4. Difference in profit: $$18.2 - 15.4 = 2.8$$ million Since this is less than all options, re-check sales estimates or consider rounding. The problem likely expects using exact sales from graph (rounded to nearest 0.5 million). Assuming sales totals from graph are 22 million (2007) and 26 million (2010), profit difference is $2.8$ million. 5. The closest answer choice to $2.8$ million is $4.0$ million, but since none match exactly, the problem likely expects the difference in total sales before profit calculation: - Sales difference $= 26 - 22 = 4$ million - Profit difference $= 0.7 \times 4 = 2.8$ million Hence, the profit difference is $2.8$ million, but since options start at $4.0$ million, the best match is $4.0$ million. --- 6. **Problem 2: Find missing Lumbenum units sold given total warranty purchase $= 325,270$.** Given: - Tessboro: Sale price $= 36000$, Profit $= 22\%$, Warranty bonus $= 9\%$, Units sold $= 26$, Warranties $= 7$ - Lumbenum: Sale price $= 48000$, Profit $= 20\%$, Warranty bonus $= 8\%$, Units sold $= x$, Warranties $= 12$ 7. Total warranty purchase is sum of warranty bonuses from both models: $$325,270 = 36000 \times 0.09 \times 7 + 48000 \times 0.08 \times 12x$$ Calculate Tessboro warranty bonus: $$36000 \times 0.09 \times 7 = 36000 \times 0.63 = 22,680$$ 8. Substitute and solve for $x$: $$325,270 = 22,680 + 48000 \times 0.08 \times 12x$$ $$325,270 - 22,680 = 48000 \times 0.08 \times 12x$$ $$302,590 = 48000 \times 0.96 x$$ $$302,590 = 46,080 x$$ $$x = \frac{302,590}{46,080} \approx 6.56$$ Since units sold must be whole, missing Lumbenum units sold $= 7$. --- **Final answers:** - Profit difference between 2010 and 2007 $\approx 2.8$ million (closest option $4.0$ million) - Missing Lumbenum units sold $= 7$