Answer to Question #168929 in Macroeconomics for KHUSHI

Question

The Blanchard family has 250 acres of land in Louisiana where they grow a rotation of three organic crops: sugarcane, tobacco, and oilseed. Each winter, the Blanchards decide how much land to devote to each crop. At least 400 tons of sugarcane, 520 tons of tobacco, and 360 tons of oilseed are needed to satisfy a futures contract they signed a few months before. They can sell sugarcane, tobacco, and oilseed for $200, $250, and $300 per ton, respectively, but would have to pay a 25% markup on those prices if they needed to buy these same crops after the harvest. The probability of a good planting season is 40% and the corresponding yields for sugarcane, tobacco, and oilseed are 8.4, 6.8, and 5.6 tons per acre, respectively. The probability of a bad season is 60% and the resulting yields would be 5, 3.4, and 2.8 tons per acre, respectively. Formulate a two-stage stochastic optimization model to maximize the Blanchard’s expected profit. How much land should be devoted to each crop to fulfill their contract (even if that means purchasing some of the crops)?

Answer 1

find a plan maximum profit:

$400\times200+520\times250+360\times300-0.25(400\times200+520\times250+360\times300)=238500$

where

$(8.4\times x\times200+6.8\times y\times250+5.6\times z\times300-0.25(8.4\times x\times200+6.8\times y\times250+5.6\times z\times300-0.25)\times0.4=max$

$(5\times x\times200+3.4\times y\times250+2.8\times z\times300-0.25(\times x\times200+3.4\times y\times250+2.8\times z\times300)\times0.6=min$

$x+y+z<250$