Problem 2 (50pts). An insurance company is introducing three products: special risk insurance, mortgage insurance, and long-term care insurance. The expected profit is $500 per unit on special risk insurance, $250 per unit on mortgage insurance and $600 per unit on long term care insurance. The work requirements are as follows: The management team wants to establish sales quotas for each product to maximize the total expected profit. 1. Formulate this problem as a linear optimization problem. Specify the decision variables, objective function, and constraints. Department Working hours per unit Working hours available Special risk Mortgage Long-term care Underwriting 2 1 1 240 Administration 1 2 150 Claims 1 2 4 180 3 B 0 50 0 0 80 0 1 4 1 3 0 0.5 1 0 0 0.5 140 -0.7 0.4 -0.1 35400 153 24 39 0 0.1 -0.2 0.3 0 1 0 2. After solving the problem, the final simplex tableau (for the standard form) is given as below (the variables are in the natural order as in the description of the problem): Show the dual variables corresponding to the services of the three departments. Using complementarity conditions to explain why mortgage insurance is not sold. 3. Find the range of working hours available for claims to keep the current basis optimal. 4. Find the range of the expected profit on special risk insurance such that the current basis remains optimal. Problem 2 (50pts). An insurance company is introducing three products: special risk insurance, mortgage insurance, and long-term care insurance. The expected profit is $500 per unit on special risk insurance, $250 per unit on mortgage insurance and $600 per unit on long term care insurance. The work requirements are as follows: The management team wants to establish sales quotas for each product to maximize the total expected profit. 1. Formulate this problem as a linear optimization problem. Specify the decision variables, objective function, and constraints. Department Working hours per unit Working hours available Special risk Mortgage Long-term care Underwriting 2 1 1 240 Administration 1 2 150 Claims 1 2 4 180 3 B 0 50 0 0 80 0 1 4 1 3 0 0.5 1 0 0 0.5 140 -0.7 0.4 -0.1 35400 153 24 39 0 0.1 -0.2 0.3 0 1 0 2. After solving the problem, the final simplex tableau (for the standard form) is given as below (the variables are in the natural order as in the description of the problem): Show the dual variables corresponding to the services of the three departments. Using complementarity conditions to explain why mortgage insurance is not sold. 3. Find the range of working hours available for claims to keep the current basis optimal. 4. Find the range of the expected profit on special risk insurance such that the current basis remains optimal
