Suppose that the refinery in Example 5 has 35,000 barrels of component A, which costs $25 a barrel, and 15,000 barrels of component B, which costs $35 a barrel. If all other data remain the same, formulate a linear programming problem to find the maximum profit. Do not attempt to solve the problem (unless you have access to software that can solve linear programming problems).

Data from Example 5

A refinery produces two grades of gasoline, regular and premium, by blending together two components, A and B. Component A has an octane rating of 90 and costs $28 a barrel. Component B has an octane rating of 110 and costs $32 a barrel. The octane rating for regular gasoline must be at least 95, and the octane rating for premium must be at least 105. Regular gasoline sells for $34 a barrel and premium sells for $40 a barrel. Currently, the company has 30,000 barrels of component A and 20,000 barrels of component B. It also has orders for 20,000 barrels of regular and 10,000 barrels of premium that must be filled. Assuming that all the gasoline produced can be sold, determine the maximum possible profit.