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【数学中国推荐】1992-2009年CUMCM优秀论文全收入

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发表于 2009-3-25 17:51 |只看该作者
|招呼Ta 关注Ta
美国的一道题不知怎么做Cobalt, which is not produced in the US, is essential to a number of industries. (Defense accounted for 17% of the cobalt production in 1979.) Most cobalt comes from central Africa, a politically unstable region. The Strategic and Critical Materials Stockpiling Act of 1946 requires a cobalt reserve that will carry the US through a three-year war. The government built up a stockpile in the 1950s, sold most of it off in the early 1970s, and then decided to build it up again in the late 1970s, with a stockpile goal of 85.4 million pounds. About half of this stockpile had been acquired by 1982. 1 ?: d5 R# C7 A
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Build a mathematical model for managing a stockpile of the strategic metal cobalt. You will need to consider such questions as: 9 k$ G2 C5 S5 A1 Y
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How big should the stockpile be?
( q8 [5 |5 B3 _At what rate should it be acquired?
! @! F0 x* a. xWhat is a reasonable price to pay for the metal?
0 \1 f2 Y8 M0 E& {- eYou will also want to consider such questions as:
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9 \7 T# b- L" ]2 `5 _; _1 TAt what point should the stockpile be drawn down? 1 ]' c( B0 _4 T1 L& |  `9 C: V
At what rate should it be drawn down? + Y/ c  }" ~6 K5 w# J" f4 M0 ]
At what price is it reasonable to sell the metal? ) m) O: \* g- s7 q% m  k
How should it be allocated?
6 i6 N: ~2 U4 N9 YUseful Information on Cobalt . @+ m) v8 G$ q  b7 x
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The government has projected a need ot 25 million pounds of cobalt in 1985.
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The U.S. has about 100 million pounds of proven cobalt deposits. Production becomes economically feasible when the price reaches $22/lb (as occurred in 1981). It takes four years to get operations rolling, and thsn six million pounds per year can be produced. 5 z* `7 @, d# d- c( g
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In 1980, 1.2 million pounds of cobalt were recycled, 7% of total consumption.
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