The Surest Concrete Company produces cement in a continuous process. Two ingredients in the cement are sand, which Surest purchases for $6 per ton, and gravel, which costs $8 per ton. The other ingredients are lumped together and referred to as "Other". The cost of the other ingredients is $5 per ton. No more than 40 percent of the cement can be sand, and at least 30 percent of the cement must be gravel. The maximum amount of gravel available is 100 tons. The maximum amount available of the "Other" ingredients is 125 tons. The cement sells for $60 per ton.
The company wants to maximize its profit.
a) Formulate the linear programming problem to maximize the profit