Question

一个半职业棒球联盟中每队有 $21$ 名球员。联盟规则规定，每名球员工资至少为 $\$15{,}000$ ，并且每队所有球员工资总和不能超过 $\$700{,}000$ 。单名球员最高可能工资是多少美元？

A semipro baseball league has teams with $21$ players each. League rules state that a player must be paid at least $\$15{,}000,$ and that the total of all players' salaries for each team cannot exceed $\$700{,}000.$ What is the maximum possible salary, in dollars, for a single player?

$270{,}000$

$385{,}000$

$400{,}000$

$430{,}000$

$700{,}000$

答案：C

知识点：不等式最优化极端原理

难度评级：840

解答：

当其他 $20$ 名球员各拿最低工资 $\$15{,}000$ 时，某一名球员工资最大。

剩下给这名球员的是 $\$700{,}000-20\cdot\$15{,}000$ $=\$700{,}000-\$300{,}000$ $=\$400{,}000$ 。

所以正确答案是 C。

One player's salary is largest when the other $20$ players each earn the minimum $\$15{,}000.$

That leaves $\$700{,}000-20\cdot\$15{,}000$ $=\$700{,}000-\$300{,}000$ $=\$400{,}000$ for the single player.

Thus, the correct answer is C.

2008 AMC 10B 第 4 题

答案：C

难度评级：840

解答：

其他年份的第 4 题