Chapter 6.4, Problem 41E

In Problems 39-47, construct a mathematical model in the form of a linear programming problem. Do not solve.

Oil refining. A refinery produces two grades of gasoline, regular and premium, by blending together three components: $A,B,$ and $C$. Component $A$ has an octane rating of $90$ and costs $\text{\$}28$ a barrel, component $B$ has an octane rating of $100$ and costs $\text{\$}30$ a barrel, and component $C$ has an octane rating of $110$ and costs $\text{\$}34$ a barrel. The octane rating for regular must be at least $95$ and the octane rating for premium must be at least $105$. Regular gasoline sells for $\text{\$}38$ a barrel and premium sells for $\text{\$}46$ a barrel. The company has $40,000$ barrels of component $A$, $25000$ barrels of component $B$, and $15,000$ barrels of component $C$. It must produce at least $30,000$ barrels of regular and $25,000$ barrels of premium. How should the components be blended in order to maximize profit?