You firm is considering in buying several companies, and then making improvements at each of these...

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You firm is considering in buying several companies, and then making improvements at each of these companies with the hope of selling at a profit. The companies are in several sectors. The sector of each company, the net present value, and the capital required to purchase each company, is given in the following table: Company Est. net present value A $50 million B $30 million с $20 million D $10 million E $15 million F $60 million G $10 million H $80 million Capital requirements $200 million $150 million $120 million $50 million $75 million $300 million $80 million $400 million 1 You decide to create an optimization problem to decide which companies to invest in. You decide to use the following variables: Sector Tech Tech Tech Retail Retail Manufacturing Manufacturing Manufacturing YA: a binary variable; 1 if you purchase company A • YB: a binary variable; 1 if you purchase company B ● etc... (a) (8 pts.) Write a linear objective function for this problem. Note that the estimated net present value accounts for the capital requirements. For example, if your firm purchases Company A, then you expect to recoup your initial investment of $200 million and make an additional $50 million dollars (in today's dollars). (b) (8 pts.) Your firm has $600 million to invest. Write a constraint that ensures that you do not invest more than this. (c) (7 pts.) There is a conflict of interest between firms D and E, so you cannot buy both of these. Write a constraint that enforces this condition. (d) (7 pts.) In order to have a diverse portfolio, you want to invest in at least one company from each sector. Write linear constraints that enforce this condition. You will need multiple constraints. You firm is considering in buying several companies, and then making improvements at each of these companies with the hope of selling at a profit. The companies are in several sectors. The sector of each company, the net present value, and the capital required to purchase each company, is given in the following table: Company Est. net present value A $50 million B $30 million с $20 million D $10 million E $15 million F $60 million G $10 million H $80 million Capital requirements $200 million $150 million $120 million $50 million $75 million $300 million $80 million $400 million 1 You decide to create an optimization problem to decide which companies to invest in. You decide to use the following variables: Sector Tech Tech Tech Retail Retail Manufacturing Manufacturing Manufacturing YA: a binary variable; 1 if you purchase company A • YB: a binary variable; 1 if you purchase company B ● etc... (a) (8 pts.) Write a linear objective function for this problem. Note that the estimated net present value accounts for the capital requirements. For example, if your firm purchases Company A, then you expect to recoup your initial investment of $200 million and make an additional $50 million dollars (in today's dollars). (b) (8 pts.) Your firm has $600 million to invest. Write a constraint that ensures that you do not invest more than this. (c) (7 pts.) There is a conflict of interest between firms D and E, so you cannot buy both of these. Write a constraint that enforces this condition. (d) (7 pts.) In order to have a diverse portfolio, you want to invest in at least one company from each sector. Write linear constraints that enforce this condition. You will need multiple constraints.