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. Fractional values of the inputs and outputs are allowed.

The company wants to maximize its profit.  

a) Formulate the liner programming problem to maximize the profit.

b) Using linear programming, solve for the optimal solution, identifying the value of the objective function and the variables at optimality. To receive credit for this answer, you must provide a copy of your linear programming output, identifying the value of the objective function and the values of the variables at optimality. You must submit your linear programming formulation and show the linear programming software solution to this problem to receive credit.

c) Using the sensitivity analysis output from part b, provide any two sensitivity analysis interpretations. One of the interpretations must relate to the objective function and the second one must relate to one of the constraints.

d) Write a constraint(s) that ensures that the cost of the “Other” ingredient is not less than 30% and not more than 40% of the total cost of the cement being provided. You only need formulate this constraint. You do not need to solve the linear programming problem for the solution.