A bank is attempting to determine where its assets should be invested during the current year. At present, $500,000 is available for investment in bonds, home loans, auto loans, and personal loans. The annual rate of returns are shown in the table below.Investment Annual Rate of Return Bonds 10 % Home Loans 16 % Auto Loans 13 % Personal Loans 20 %To ensure that the bank’s portfolio is not too risky, the bank’s investment manager has placed the following three restrictions on the banks portfolio:· The amount invested in personal loans cannot exceed the annual amount invested in bonds.· The amount invested in home loans cannot exceed the amount invested in auto loans· No more than 25% of the total amount invested can be in personal loans. Formulate and solve this problem in Excel to determine how the bank should invest in assets to meet the requirements and maximize the annual return of its investment portfolio.a) How many decision variables does this problem have?b) Not counting the non-negativity constraint – how many constraints does this problem have?c) What is the total return for the investments based on your optimal solution (the value of the objective function)?d) How much should be invested in Bonds based on your optimal solution?e) How much should be invested in Home Loans based on your optimal solution?f) How much should be invested in Auto Loans based on your optimal solution?g) How much should be invested in Personal Loans based on your optimal solution?
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