Chapter 6.4, Problem 40E

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

Loan distributions. A savings and loan company has $\text{\$}3$ million to lend. The types of loans and annual returns offered are given in the table. State laws require that at least $50\text{\%}$ of the money loaned for mortgages must be for first mortgages and that at least $30\text{\%}$ of the total amount loaned must be for either first or second mortgages. Company policy requires that the amount of signature and automobile loans cannot exceed $25\text{\%}$ of the total amount loaned and that signature loans cannot exceed $15\text{\%}$ of the total amount loaned. How much money should be allocated to each type of loan in order to maximize the company’s return?