2. (30 points) Consider an integer program which models a manufacturing scenario in which profit is to be maximized. You have the decision variables Ik =(number of product type k to manufacture, k = 1,2,..., 10) and z is the profit function. You have typical resource constraints Ax 0. Model the following additional constraints. (a) If any of products of type k= 3 or k = 4 are to be manufactured, then a single machine must be rented at a fixed cost of p dollars. (b) If more than 30 of product type k = 1 are manufactured, then at least 10 of product type k = 2 must also be manufactured. (c) If any of product type k = 7 are manufactured, then at least 10 must be manufactured. That is, 1 0. Model the following additional constraints. (a) If any of products of type k= 3 or k = 4 are to be manufactured, then a single machine must be rented at a fixed cost of p dollars. (b) If more than 30 of product type k = 1 are manufactured, then at least 10 of product type k = 2 must also be manufactured. (c) If any of product type k = 7 are manufactured, then at least 10 must be manufactured. That is, 1