Montana Pulp (MP) produces recycled paperboard by combining four grades of recycled paper stock. Each grade of stock has a different strength, color, and texture. The strength, color, and texture of the finished paperboard are a weighted average of those characteristics of the paper stock inputs. The table provides the characteristics of the paper inputs and their costs per ton. An order for 500 tons of paperboard with a strength of at least 7, a color of at least 5, and a texture of at least 6 has been received. MP needs to find the minimal-cost mix of inputs required to satisfy this order.

                        

(a) Formulate an LP to minimize the cost of the order.
(b) Set up and solve the problem on a spreadsheet.
(c) What is the optimal solution? Explain the rationale for the solution.