A farmer's family is making plans for the year's planting. Its members are considering planting corn, tomatoes, potatoes, and strawberries. They have 50 acres to plant on. The aim is to determine what it costs to plant an acre of each crop, computing the yield in bushels, forecasting the revenue for a bushel of each crop, and choosing the combination of crops that will yield the most profit. The data they have collected, along with the availability of resources, is shown in the table.
|
Crop
|
Yield/Acre (bushels)
|
Revenue/ Bushel
|
Planting Time Required (hours)
|
Tending Time Required per Week
|
Required Feet of Water per Acre /Season
|
Fertilizer Required per Acre (pounds)
|
Harvest Time Required (hours)
|
|
Corn
|
50
|
$90
|
10
|
2
|
2.5
|
50
|
6
|
|
Tomatoes
|
38
|
$210
|
15
|
8
|
3
|
60
|
20
|
|
Potatoes
|
45
|
$50
|
12
|
2
|
2
|
45
|
9
|
|
Strawberries
|
56
|
$56
|
18
|
12
|
3
|
35
|
20
|
|
|
|
Total Available
|
770
|
550
|
300
|
3000
|
770
|
a) Determine the best mix of crops to maximize their revenue.
b) The farmers also have the opportunity to buy a 78-acre farm adjacent to their land. They would like to narrow their selection of crops to corn, strawberries, or a combination of the two. If they acquire the land, they will be able to increase the time available to 1,800 hours for planting, 825 hours for tending, and 1,400 hours for harvesting. All these increases are from the available limits in part (a). Between the two farms, there is 510 acre-feet of water available for the season. The farmers can obtain up to 7,000 pounds of fertilizer. The new farm has not been cultivated in a while, so the farmers believe that each acre of the new farm will take an extra 4 hours of labor to plant, and an extra 2 hours per acre to tend. Because of the condition of the new farm, they expect the yields to be down from 50 to 45 bushels per acre for corn and from 56 to 50 bushels per acre for strawberries. They want to know the best combination of crops to plant on each farm, with the goal to maximize revenue from at least 75% of each farm's acreage.