For all students: Formulate the following problem into a mathematical optimization problem.

First, state clearly the decision variables$),$ objective, and constraints $($if any$).$ Then, use

mathematical notations of your choice for the decision variables, and express the objective and

constraints as functions of the decision variables.

Materials. A contractor can sell several classes of concrete at a different price per$-$ton

for each class. The materials specification for each class of concrete allows the percent$-$

age by weight of cement, sand, and gravel to range between certain upper and lower

bounds. The contractor knows the unit cost $($cost per$-$pound$)$ to the company for each

of the three components of concrete, and how much of each component that is avail$-$

able for the company to purchase. The amount of concrete of each type that the con$-$

tractor can sell is limited but known. $($Hint: This problem has a maximization obiective

function, not minimization.$)$