Dust James owns and operates a 300-acre farm in northern Maine. Having recently abandoned potato growing. Dusty plans to grow wheat, corn, oats, and soybeans, for the upcoming season. he wishes to grow at least 30,000 bushels of wheat, 25,000 bushels of corn, and no more than 25,00 of oats. dusty also has up to 1800 hours of of labor, a 1200 acre-ft water supply, and a budget limitation of $25,000. The table below contains data pertaining to yield, requirements, expenses, and prices.
|
Crop
|
Yield (bu/acre)
|
Labor Requirements (hr/acre)
|
Expenses ($/acre)
|
Water Requirements (acre-ft/acre)
|
Price ($/bu)
|
|
Wheat
|
210
|
4
|
$50
|
2
|
$3.20
|
|
Corn
|
300
|
5
|
$75
|
6
|
$2.55
|
|
Oats
|
180
|
3
|
$30
|
1
|
$1.45
|
|
Soybeans
|
240
|
10
|
$60
|
6
|
$3.10
|
The unit profit per acre = yield/acre X price/acre - expenses/acre [ e.g, for wheat: 210( $3.20) - $50 = $622 ].
Dusty wishes to determine how many acres allocated to maximize his profit. ( Hint: let Xi be the # of acres allocated to growing crop I; I = wheat, corn, oats, soybeans).
1) Formulate the above problem as a linear program in order to maximize profit for the upcoming growing season, ( just formulate, don't solve).
2) Solve using the simplex method, and state the optimal solution. Attach a coputer printout.