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：最优化极端原理

难度评级：1100

解答：

当其他 $20$ 名球员每人都拿最低工资 $\$15{,}000$ 时，一名球员的工资最大。

因此最大工资为 $\$700{,}000$ $- 20 \cdot \$15{,}000$ $= \$700{,}000$ $- \$300{,}000$ $= \$400{,}000$ 。

因此，正确答案是 C。

One player earns the most when the other $20$ players each receive the minimum salary of $\$15{,}000.$

Thus the maximum salary is $\$700{,}000$ $- 20 \cdot \$15{,}000$ $= \$700{,}000$ $- \$300{,}000$ $= \$400{,}000.$

Thus, the correct answer is C.

2008 AMC 12B 第 3 题

答案：C

难度评级：1100

解答：

其他年份的第 3 题