4. (10 points) A fund manager is considering a portfolio for his customer. He has identified 12 invest- ment projects, which require different amounts of capital and generate different profits. He need to decide which projects to take to maximize the total profits. Let Q dollars be the total investment budget of the customer, and let P, and C; denote, respectively, the profit and capital in dollars) required for project i (i = 1,...,12). The decision is also subjected to the following concerns: If project 4 is undertaken, then project 2 must be undertaken; Project 3 cannot be undertaken unless projects 10, 11 and 12 are all undertaken; Project 7 and project 12 cannot be both taken; The projects 8, 9 and 10 are all undertaken if and only if project 4 is undertaken; At least three and at most six investments have to be undertaken from projects 1, 2, 3, 5, 6, 7, 9, 11; If projects 4 or 7 are undertaken, then project 10 cannot be undertaken. Formulate this problem using a binary integer programming model. You are not required to solve this