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A farm family owns 50 acres of land & has $ 7,000 ava

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Microsoft Word - 412LP-FarmProb-Abdu.doc

A farm family owns 50 acres of land & has $ 7,000 available for investment every year. Its members can produce a total of 3600 worker-hr. of labor during winter months & 4100 worker-hr. during summer. The family members can also work on a neighboring farm for $ 5/hr during the winter months and $ 7/hr during the summer. In addition to the salary they can make from working at the neighbors farms, income may also be obtained from three crops and two types of livestock: dairy cows and laying hens. Land, investment funds & worker-hours required as well as the annual income for the crops and livestock are as follows:

A farm family owns 50 acres of land & has $ 7,000 available for investment every year.

 

Its members can produce a total of 3600 worker-hr. of labor during winter months &

 

4100 worker-hr. during summer. The family members can also work on a neighboring

 

farm for $ 5/hr during the winter months and $ 7/hr during the summer. In addition to the

 

salary they can make from working at the neighbors farms, income may also be obtained

 

from three crops and two types of livestock: dairy cows and laying hens. Land,

 

investment funds & worker-hours required as well as the annual income for the crops

 

and livestock are as follows:

 

Type of Crop or

 

Income

 

Requirements

 

Livestock

 

$/year

 

Acres per Worker-hours

 

Cost

 

year

 

$/year

 

Winter

 

Summer

 

Cows

 

1.5

 

50

 

30

 

800

 

1800

 

Hens

 

0

 

0.6

 

0.3

 

1

 

4

 

Soybeans/acre

 

1

 

15

 

25

 

60

 

960

 

Corn/acre

 

1

 

25

 

50

 

100

 

1400

 

Oats/acre

 

1

 

10

 

20

 

50

 

1150

 

The chicken house can accommodate a maximum of 120 hens, and the size of the barn

 

limits the herd to a maximum of 20 cows. Formulate and solve to determine how much

 

acreage should be planted in each of the crops and how many cows and hens should be

 

kept, as well as the hours worked at the neighbors farms, to maximize the net annual

 

income.

 

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Sep 21, 2019

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