(Investment): An investor has $150,000 to invest in oil stock, steel stock, and government bonds. The bonds are guaranteed to yield 5%, but the yield for each stock can vary. To protect against major losses, the investor decides that the amount invested in oil stock should not exceed $50,000. The total amount invested in stock CANNOT exceed the amount invested in bonds by more than $25,000.

a) Set up the problem (decision variables, problem constraints, non-negativity constraints).

b) Now form the objective function if oil stock yields 12% and the steel stock yields 9%. How much should be invested in each alternative in order to maximize the return (don't forget the bonds). What is the maximum return?

Please solve using the bigM simplex method, involving slack, surplus, and artificial variables.