AMC12 2003 B

AMC12 2003 B · Q3

AMC12 2003 B · Q3. It mainly tests Arithmetic misc, Optimization (basic).

Rose fills each of the rectangular regions of her rectangular flower bed with a different type of flower. The lengths, in feet, of the rectangular regions in her flower bed are as shown in the figure. She plants one flower per square foot in each region. Asters cost $\$1$ each, begonias $\$1.50$ each, cannas $\$2$ each, dahlias $\$2.50$ each, and Easter lilies $\$3$ each. What is the least possible cost, in dollars, for her garden?

Rose 在她的矩形花坛中，把每个矩形区域都种上不同种类的花。图中给出了花坛中各矩形区域的长度（单位：英尺）。她在每个区域中每平方英尺种一朵花。紫菀每朵 $\$1$，秋海棠每朵 $\$1.50$，美人蕉每朵 $\$2$，大丽花每朵 $\$2.50$，复活节百合每朵 $\$3$。她的花园最少可能花费多少美元？

(A) 108 108

(B) 115 115

(D) 144 144

(E) 156 156

Answer

Correct choice: (A)

正确答案：（A）

Solution

The areas of the five regions from greatest to least are $21,20,15,6$ and $4$. If we want to minimize the cost, we want to maximize the area of the cheapest flower and minimize the area of the most expensive flower. Doing this, the cost is $1\cdot21+1.50\cdot20+2\cdot15+2.50\cdot6+3\cdot4$, which simplifies to $\$$108$. Therefore the answer is $\boxed{\textbf{(A) } 108}$.

五个区域的面积从大到小分别是 $21,20,15,6$ 和 $4$。为了使花费最小，应让最便宜的花对应的面积最大，让最贵的花对应的面积最小。这样总花费为 $1\cdot21+1.50\cdot20+2\cdot15+2.50\cdot6+3\cdot4$，化简得 $\$$108$。因此答案是 $\boxed{\textbf{(A) } 108}$。

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