A company is planning the production next week. The company has seven types of products. Each type of product has a profit (SGD) per unit and a production time (hours) per unit as shown below. The total number of hours available next week is 420 hours. To maximize the profit of the next week, 1 2 3 4 5 6 7 Product type Unit profit 10 22 35 19 55 10 115 Production time 1 2 3.7 2.4 4.5 0.7 9.5 if any of type-7 or type-6 product is produced, an additional fixed cost of 2000 SGD is incurred. (Remark: If both type-7 and type-6 products are produced, the fixed cost is still 2000 SGD, not 4000 SGD.) Please formulate a mixed integer program- ming problem to maximize the company's profit. Please also solve the problem with Matlab CVX or Excel, and write down how many product of each type should be produced. (You do not need to attach the codes.)