The Ploughman family owns and operates a 640 -acre farm that has been in the family for several generations. The Ploughmans always have had to work hard to make a decent living from the farm and have had to endure some occasional difficult years. Stories about earlier generations overcoming hardships due to droughts, floods, etc., are an important part of the family history. However, the Ploughmans enjoy their selfreliant lifestyle and gain considerable satisfaction from continuing the family tradition of successfully living off the land during an era when many family farms are being abandoned or taken over by large agricultural corporations.
Ploughman 家族拥有并经营着一个 640 英亩的农场，该农场已经由家族几代人经营。Ploughmans 总是不得不努力工作以在农场过上体面的生活，并且不得不偶尔忍受一些艰难的岁月。关于前几代人克服干旱、洪水等困难的故事，是家族历史的重要组成部分。然而，Ploughmans 享受着自力更生的生活方式，并在许多家庭农场被废弃或被大型农业公司接管的时代，继续成功地靠土地生活的家族传统获得了相当大的满足感。

John Ploughman is the current manager of the farm while his wife Eunice runs the house and manages the farm’s finances. John’s father, Grandpa Ploughman, lives with them and still puts in many hours working on the farm. John and Eunice’s older children, Frank, Phyllis, and Carl, also are given heavy chores before and after school.
John Ploughman 是农场的现任经理，而他的妻子 Eunice 则负责管理房子并管理农场的财务。John 的父亲 Ploughman 爷爷和他们住在一起，仍然在农场工作很多时间。John 和 Eunice 的大孩子 Frank、Phyllis 和 Carl 在放学前和放学后也要做繁重的家务活。

The entire famiy can produce a total of 4,000 person-hours worth of labor during the winter and spring months and 4,500 person-hours during the summer and fall. If any of these person-hours are not needed, Frank, Phyllis, and Carl will use them to work on a neighboring farm for $\mathrm{\$}5$$\mathrm{\$}5$$5\$ 5 per hour during the winter and spring months and $\mathrm{\$}5.50$$\mathrm{\$}5.50$$5.50\$ 5.50 per hour during the summer and fall.
整个家庭在冬季和春季总共可以生产 4,000 人小时的劳动力，在夏季和秋季可以生产 4,500 人小时的劳动力。如果不需要这些工时中的任何一个，Frank、Phyllis 和 Carl 将在冬季和春季使用它们在邻近的农场 $\mathrm{\$}5$$\mathrm{\$}5$$5\$ 5 工作，在夏季和秋季 $\mathrm{\$}5.50$$\mathrm{\$}5.50$$5.50\$ 5.50 按小时计算。

The farm supports two types of livestock: dairy cows and laying hens, as well as three crops: soybeans, corn, and wheat. (All three are cash crops, but the corn also is a feed crop for the cows and the wheat also is used for chicken feed.) The crops are harvested during the late summer and fall. During the winter months, John, Eunice, and Grandpa make a decision about the mix of livestock and crops for the coming year.
该农场饲养着两种类型的牲畜：奶牛和蛋鸡，以及三种作物：大豆、玉米和小麦。（这三种作物都是经济作物，但玉米也是奶牛的饲料作物，小麦也用作鸡饲料。农作物在夏末和秋季收获。在冬季，约翰、尤妮丝和爷爷会决定来年的牲畜和农作物的组合。

Currently, the family has just completed a particularly successful harvest which has provided an investment fund of $\mathrm{\$}20,000$$\mathrm{\$}20,000$$20,000\$ 20,000 that can be used to purchase more livestock. (Other money is available for ongoing expenses, including the next planting of crops.) The family currently has 30 cows valued at $\mathrm{\$}35,000$$\mathrm{\$}35,000$$35,000\$ 35,000 and 2,000 hens valued at $\mathrm{\$}5,000$$\mathrm{\$}5,000$$5,000\$ 5,000. They wish to keep all this livestock and perhaps purchase more. Each new cow would cost $\mathrm{\$}1,500$$\mathrm{\$}1,500$$1,500\$ 1,500, and each new hen would cost $\mathrm{\$}3$$\mathrm{\$}3$$3\$ 3.
目前，这个家庭刚刚完成了一次特别成功的收成，这为他们提供了一个投资基金 $\mathrm{\$}20,000$$\mathrm{\$}20,000$$20,000\$ 20,000 ，可以用来购买更多的牲畜。（其他资金可用于持续开支，包括下一次种植农作物。该家族目前拥有 30 头奶牛 $\mathrm{\$}35,000$$\mathrm{\$}35,000$$35,000\$ 35,000 和 2,000 只母鸡。 $\mathrm{\$}5,000$$\mathrm{\$}5,000$$5,000\$ 5,000 他们希望保留所有这些牲畜，也许还会购买更多。每头新奶牛的成本 $\mathrm{\$}1,500$$\mathrm{\$}1,500$$1,500\$ 1,500 为 ，每只新母鸡的成本 $\mathrm{\$}3$$\mathrm{\$}3$$3\$ 3 为 。

Over a year’s time, the value of a herd of cows will decrease by about 10 percent and the value of a flock of hens will decrease by about 25 percent due to aging.
在一年的时间里，由于老化，一群奶牛的价值将下降约 10%，而一群母鸡的价值将下降约 25%。

Each cow will require 2 acres of land for grazing and 10 person-hours of work per month, while producing a net annual cash income of $\mathrm{\$}850$$\mathrm{\$}850$$850\$ 850 for the family. The corresponding figures for each hen are: no significant acreage, 0.05 person-hour per month, and an annual net cash income of $\mathrm{\$}4.25$$\mathrm{\$}4.25$$4.25\$ 4.25. The chicken house can accommodate a maximum of 5,000 hens, and the size of the barn limits the herd to a maximum of 42 cows.
每头奶牛每月需要 2 英亩的土地用于放牧和 10 个工时的工作，同时为家庭产生每年的净现金收入 $\mathrm{\$}850$$\mathrm{\$}850$$850\$ 850 。每只母鸡对应的数字是：无大面积，每月 0.05 人小时，年现金净收入 $\mathrm{\$}4.25$$\mathrm{\$}4.25$$4.25\$ 4.25 。鸡舍最多可容纳 5,000 只母鸡，谷仓的大小将牛群限制为最多 42 头奶牛。

For each acre planted in each of the three crops, the following table gives the number of person-hours of work that will be required during the first and second halves of the year, as well as a rough estimate of the crop’s net value (in either income or savings in purchasing feed for the livestock).
对于三种作物中每种植一英亩的土地，下表给出了一年上半年和下半年所需的工作工时数，以及作物净值的粗略估计（收入或购买牲畜饲料的储蓄）。

To provide much of the feed for the livestock, John wants to plant at least 1 acre of corn for each cow in the coming year’s herd and at least 0.05 acre of wheat for each hen in the coming year’s flock.
为了给牲畜提供大部分饲料，John 希望为来年牛群中的每头奶牛种植至少 1 英亩的玉米，为来年羊群中的每只母鸡至少种植 0.05 英亩的小麦。

John, Eunice, and Grandpa now are discussing how much acreage should be planted in each of the crops and how many cows and hens to have for the coming year. Their objective is to maximize the family’s monetary worth at the end of the coming year (the sum of the net income from the livestock for the coming year plus the net value of the crops for the coming year plus what remains from the investment fund plus the value of the livestock at the end of the coming year plus any income from working on a neighboring farm, minus living expenses of $\mathrm{\$}40,000$$\mathrm{\$}40,000$$40,000\$ 40,000 for the year).
约翰、尤尼斯和爷爷现在正在讨论每种作物应该种植多少面积，以及来年应该有多少头牛和母鸡。他们的目标是在来年年底使家庭的货币价值最大化（来年牲畜的净收入加上来年的农作物净值，加上投资基金的剩余部分，加上来年年底的牲畜价值，加上在邻近农场工作的任何收入的总和）， 减去当年的生活费 $\mathrm{\$}40,000$$\mathrm{\$}40,000$$40,000\$ 40,000 ）。