An investment firm received ₹120,000 from a client for investment. The firm has identified six options and their expected returns are as given in the following table. Each option needs a minimum entry amount for that investment as given in the cost column.

Investment managers also identified certain conditions for investment. Option 2 can be chosen if and only if Option 4 and Option 6 are chosen. Option 3 can be chosen if and only if Option 1 or Option 5 or both options are selected. The investment firm wants to determine the optimum portfolio to maximize its return.
a. Formulate an integer programming model for this problem.
b. Solve this model by using the computer. 

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Options 1 2 3 4 5 6 Cost (in thousands) 26 24 35 32 26 32 Yearly Return (in thousands) 2.3 3 4 4.2 2.4 3