A savings and loan company has $3 million to lend. The types of loans and annual returns offered are given in the table. State laws require that at least 50% of the money loaned for mortgages must be for first mortgages and that at least 30% 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% of the total amount loaned and that signature loans cannot exceed 15% of the total amount loaned. How much money should be allocated to each type of loan in order to maximize the company's return?

In Problem, construct a mathematical model in the form of a linear programming problem.

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Type of Loan Signature First mortgage Second mortgage Automobile Annual Return (%) 18 12 14 16