dolution

Mike won a $30,000 prize that %10 will be reduced for taxes. He wants to invest the rest of the money and offered two opportunities. The first offer requires $20,000 and he has to spend two days a week. The second option needs 3 days a week work while investing $25,000 investment. The profit from first and second investments is estimated to be $30,000 and $40,000 respectively. One of his friends also offered another profitable investment option that needs $10,000, but he should work 4 days a week. This investment will be very profitable, and its estimated profit is $50,000. He can choose only one option or a fraction of a full partnership in each investment option.

Part a) Formulate the problem using linear programming.

Part b) Find the best investment strategy when he only wants to spend 2 days a week for his new investments. If he wants to spend one more day, how much his profit will increase. Part

c) State the dual problem to this problem and explain its relationship with the primary problem. Part

d) Implement sensitivity analysis on profit of the first investment (You need to show a screen shot copy of your Solver page/Python code)