Q2 : AGRICULTURE. BP Farms is a 300-acre farm located near Lawrence, Kansas, owned and operated exclusively by Bill Pashley. For the upcoming growing season, Bill will grow wheat, corn, oats, and soybeans. The following table gives relevant data concerning expected crop yields, labor required, expected preharvested expenses, and water required (in addition to the forecasted rain). Also included is the price per bushel Bill expects to receive when the crops are harvested. Water (acre-ft./ acre) Yield Labor Expenses (S/acre) Price Crop (bu./acre) (hr./acre) (S/bu.) Wheat 210 4 $50 2 $3.20 Corn 300 $75 6. $2.55 Oats 180 3 $30 1 $1.45 Soybeans 240 10 $60 4 $3.10 Bill wishes to produce at least 30,000 bushels of wheat and 30,000 bushels of corn, but no more than 25,000 bushels of oats. He has $25,000 to invest in his crops, and he plans to work up to 12 hours per day during the 150-day season. He also does not wish to exceed the base water supply of 1200 acre-feet allocated to him by the Kansas Agriculture Authority. Formulate the problem for BP Farms as a linear program model that determine the optimal number of acres of each crop Bill should plant in order to maximize his total expected return from the harvested crops.

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Q2 : AGRICULTURE. BP Farms is a 300-acre farm located near Lawrence, Kansas, owned and
operated exclusively by Bill Pashley. For the upcoming growing season, Bill will grow wheat, corn,
oats, and soybeans. The following table gives relevant data concerning expected crop yields,
labor required, expected preharvested expenses, and water required (in addition to the
forecasted rain). Also included is the price per bushel Bill expects to receive when the crops are
harvested.
Water
(acre-ft./
acre)
Yield
Labor
Expenses
(S/acre)
Price
Crop
(bu./acre)
(hr./acre)
(S/bu.)
Wheat
210
4
$50
$3.20
Corn
300
$75
6.
$2.55
Oats
180
3
$30
1
$1.45
Soybeans
240
10
$60
4
$3.10
Bill wishes to produce at least 30,000 bushels of wheat and 30,000 bushels of corn, but no more
than 25,000 bushels of oats. He has $25,000 to invest in his crops, and he plans to work up to 12
hours per day during the 150-day season. He also does not wish to exceed the base water supply
of 1200 acre-feet allocated to him by the Kansas Agriculture Authority.
Formulate the problem for BP Farms as a linear program model that determine the optimal
number of acres of each crop Bill should plant in order to maximize his total expected return from
the harvested crops.
Transcribed Image Text:Q2 : AGRICULTURE. BP Farms is a 300-acre farm located near Lawrence, Kansas, owned and operated exclusively by Bill Pashley. For the upcoming growing season, Bill will grow wheat, corn, oats, and soybeans. The following table gives relevant data concerning expected crop yields, labor required, expected preharvested expenses, and water required (in addition to the forecasted rain). Also included is the price per bushel Bill expects to receive when the crops are harvested. Water (acre-ft./ acre) Yield Labor Expenses (S/acre) Price Crop (bu./acre) (hr./acre) (S/bu.) Wheat 210 4 $50 $3.20 Corn 300 $75 6. $2.55 Oats 180 3 $30 1 $1.45 Soybeans 240 10 $60 4 $3.10 Bill wishes to produce at least 30,000 bushels of wheat and 30,000 bushels of corn, but no more than 25,000 bushels of oats. He has $25,000 to invest in his crops, and he plans to work up to 12 hours per day during the 150-day season. He also does not wish to exceed the base water supply of 1200 acre-feet allocated to him by the Kansas Agriculture Authority. Formulate the problem for BP Farms as a linear program model that determine the optimal number of acres of each crop Bill should plant in order to maximize his total expected return from the harvested crops.
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