Chapter 6, Problem 38RE

In problems 38-41, construct a mathematical model in the form of a linear programming problem (The answer in the back of the book for these application problems include the model.) Then solve the problem by the simplex, dual problem, or big $M$ methods.

Investment. An investor has $\text{\$}150,000$ to invest in oil stock, steel stock, and government bonds. The bonds are guaranteed to yield $5\text{\%}$, 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 $\text{\$}50,000$ and that the total amount invested in stock cannot exceed the amount invested in bonds by more than $\text{\$}25,000$.

(A) If the oil stock yields $12\text{\%}$ and the steel stock yields $9\text{\%}$, how much money should be invested in each alternative in order to maximize the return? What is the maximum return?

(B) Repeat part (A) if the oil stock yields $9\text{\%}$ and the steel stock yields $12\text{\%}$.