1. A farmer is looking to divide to plant different cultures. Traditionally, corn fields returned $3.50 per square meter. Oat fields returned $2.75 per square meter. Orchards produced revenues of $4.50 per square meter. The farmer has a land of 1 million square meters. In order to feed his farm animals, the cultivator must dedicate a minimum of 300,000 square meters to the culture of corn and oats together. However, since corn is more susceptible to long periods of drought, he does not want this culture to occupy more than 200,000 square meters. Lastly, he would like to allot the same amount of space to oats and orchards. a- Build a mathematical model to maximize the profit. (20 pts) b- Make the following changes to your mode: bl- If corn is planted, the land allocated to corn cannot be less than 50,000 square meters. (5 pts) b2- The farmer cannot allot land to more than two different cultures (corn, oat, orchard). (5 pts) b3- If the farmer plants corn, he has to allocate land to orchards as well. In such a case the allocated land has to be at least 20,000 square meters. (5 pts) b4- If land is allocated to corn and orchard, then oat cannot be planted. (5 pts)