Recall: x, y Z means that the decision variables x, y must be integers. 1. Farmer's dilemma Rienzi Farms grows sugar cane and soybeans on its 500 acres of land. An acre of soybeans brings a $1000 contribu- tion to overhead and profit; an acre of sugar cane has a contribution of $2000. Because of a government program no more than 200 acres may be planted in soybeans. During the planting season 1200 hours of planting time will be available. Each acre of soybeans requires 2 hours, while each acre of sugar cane requires 5 hours. The company seeks maximum contribution (profit) from its planting decision. Formulate the problem as a linear program using the following decision variables: b : Number of acres of soybeans to plant c : Number of acres of sugar cane to plant a) max1000b+2000csubjectto:b200;2b+5c500;b+c1200;b,c0 (b) max1000b+2000csubjectto:b200;2b+5c1200;b+c500;b,c0 (c) max1000b+2000csubjectto:b200;2b+5c1200;b+c500;b,c0;b,cZ (d) max2000b+1000csubjectto:b200;2b+5c1200;b+c500;b,c0;b,cZ