2. LP model and graphical method (30 points: 15 points modeling, 15 points solving) Following the 5 steps introduced in class, model the following problem as a linear program and solve it by the graphical method (a template is provided in Figure 2, next page). A company manufactures two types of cups. Cup 1 requires 1 unit of material 1 and 2 units of material 2. Cup 2 requires 4 unit of material 1 and 2 units of material 2. A cup 1 contributes $2 to profit, and a cup 2 contributes $3. The company has 100 units of material 1 and 80 units of material 2. There is no limit for the demand of cup 2, while the customer is not willing to buy more than 30 cup 1. The management team wants to maximize the profits this company. 2.2) Please use graphical method to solve the model (clearly indicate the optimal solution). X X1 Figure 2. Template for graphical method