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 return on each type of investment is known to be: bonds 10%; home loans 16%; auto loans 13%; personal loans 20%. To ensure that the bank's portfolio is not too risky, the following three restrictions are placed: (1) The amount invested in personal loans cannot exceed the amount invested in bonds. (2) The amount invested in home loans cannot exceed the amount invested in auto loans. (3) No more than 25% of the total amount invested may be in personal loans. The bank's objective is to maximize the annual rate of return on its investment, in other words, maximizing total profit. Let B, H, A, P be the amounts invested in bonds, home loans, auto loans and personal loans, respectively. What would be the total profit if only $400,000 can be invested? Show your work and describe your reasoning. What would be the profit if the interest on home loans is 14% (instead of 16%)? Show your work and describe your reasoning What would be the profit if the interest on home loans is 12% (instead of 16%)? Show your work and describe your reasoning. Write the dual model of the problem. Determine the optimal solution of the dual problem without actually solving it. Show your work and describe your reasoning. The optimal simplex tableau of the primal problem is given below. Determine the missing values. Show your work and describe your reasoning