An oil company produces gasoline from five inputs. The cost, density, viscosity, and sulfur content, and the number of barrels available of each input are listed in the file P04_78.xlsx. Gasoline sells for $72 per barrel. Gasoline can have a density of at most 0.98 units per barrel, a viscosity of at most 37 units per barrel, and a sulfur content of at most 3.7 units per barrel.

a. How can the company maximize its profit?

b. Describe how the optimal solution to the problem changes as the price of gasoline ranges from $65 to $80 per barrel.