How many acres of soybean and how many acres of corn should be planted to maximize profit?

Question

Rayland's farm grows soybeans and corns on it's 500 acres of land. An acre of soybean brings  $100 profit and an acre of corn brings  $200 profit. Because of the government program, 1200 hours of planting time will be available. Each acre of soybean requires 2 hours  while each acre of corn requires 6 hours. 

Answer 1

If only corn is planted, you could only plant 1200/6 = 200 acres at a profit of $400. For every acre of corn you didn't plant, you could plant 3 acres of soybeans in the same amount of time, increasing profit by $100. Each acre of corn replaced with soybeans uses 2 additional acres. To use the additional 300 acres that were unused when planting just corn, you would plant 150 fewer acres of corn while gaining 450 acres of soybeans. So the maximum profit is 50 acres of corn (profiting $100) and 450 acres of soybeans (profiting $450).