Question 1181443: PLEASE HELP ME TO SOLVE THIS FOLLOWING QUESTION
We consider a farmer who has a total of 500 acres of land available
for growing wheat, corn and sugar beets. We denote by x1; x2; x3 the
amount of acres of land devoted to wheat, corn and sugar beets, respectively.
The planting costs per acre are $ 150, $ 230, and $ 260 for wheat, corn
and sugar beets.
The farmer needs at least 200 tons (T) of wheat and 240 T of corn for
cattle feed which can be grown on the farm or bought from a wholesaler.
We refer to y1; y2 as the amount of wheat resp. corn (in tons) purchased
from a wholesaler. The purchase prices of wheat resp. corn per ton are
$ 238 for wheat and $ 210 for corn.
The amount of wheat and corn produced in excess will be sold at prices
of $ 170 per ton for wheat and $ 150 per ton for corn. For sugar beets
there is a quota on production which is 6000 T for the farmer. Any
amount of sugar beets up to the quota can be sold at $ 36 per ton, the
amount in excess of the quota is limited to $ 10 per ton. We denote by
w1 and w2 the amount in tons of wheat resp. corn sold and by w3; w4
the amount of sugar beets sold at the favorable price and the reduced
price, respectively.
The farmer knows that the average yield on his land is 2.5 T, 3.0 T
and 20.0 T per acre for wheat, corn and sugar beets.
Answer by ikleyn(52818)   (Show Source):
You can put this solution on YOUR website! .
This problem, with exactly the same words/numbers, is discussed/solved in these sources
http://cgm.cs.mcgill.ca/~avis/courses/567/notes/stoch1.pdf
http://user.engineering.uiowa.edu/~dbricker/Stacks_pdf1/SLPwR_Farmer.pdf
https://webspace.science.uu.nl/~akker103/ALP/stochprogfarmer.pdf
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