Please answer Problem 4 only , thanks !

Problem 1. (25 scores) 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, Product type 1 2 3 4 5 6 7 Unit profit 10 22 35 19 55 10 115 Production time 1 2 3.7 2.4 4.5 0.7 9.5 how should the company plan the production? Please formulate the problem as an integer programming problem. 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 for this.) Problem 4. (25 scores) In addition to the settings of Problem 1, the company can produce at most 500 type-6 product. If the company produce any of type-2 product, then it will not be able to produce type-3 product. Please formulate a mixed integer programming 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 for this.) Problem 1. (25 scores) 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, Product type 1 2 3 4 5 6 7 Unit profit 10 22 35 19 55 10 115 Production time 1 2 3.7 2.4 4.5 0.7 9.5 how should the company plan the production? Please formulate the problem as an integer programming problem. 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 for this.) Problem 4. (25 scores) In addition to the settings of Problem 1, the company can produce at most 500 type-6 product. If the company produce any of type-2 product, then it will not be able to produce type-3 product. Please formulate a mixed integer programming 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 for this.)