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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.
Solution details
Solution #00070166
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DATE ANSWEREDOct 14, 2020
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