1. Widget Plus stores its widgets at three warehouses, located in Richmond, VA, Atlanta, GA, and Baltimore, MD. The widgets are shipped to four different customers. The available supply at the warehouses, the customers' demands, and the unit shipping costs are shown in the table below. Warehouse Customer 1 Customer 2 Customer 3 Customer 4 | Supply $30 $20 $18 $25 420 610 ETTTIL Richmond $22 $17 Atlanta Baltimore $15 $35 $21 Demand 520 250 $16 $14 340 400 380 Additional widgets are not available, so some customers will not get all the widgets they require. Also, no customer should receive more widgets than requested. Widget Plus would like to use nonpreemptive goal programming to determine a compromise plan for distributing the widgets to the customers. Widget Plus has established the following goals: Goal 1: Customer 2 should receive all the widgets it requested. Goal 2: Ship at least 80 widgets from Baltimore to Customer 4. Goal 3.1: Meet at least 80% of Customer 1's demand. Goal 3.2: Meet at least 80% of Customer 2's demand. Goal 3.3: Meet at least 80% of Customer 3's demand. Goal 3.4: Meet at least 80% of Customer 4's demand. Goal 4: Total transportation costs should not exceed $24,750. Goal 5: Ship no units from Atlanta to Customer 1. Goal 1 is twice as important as Goal 2. Goal 2 is three times as important as Goal 3.1. Goals 3.1, 3.2, 3.3, and 3.4 are equally important. Goal 3.4 is twice as important as Goal 4. Goal 4 is three times as important as Goal 5. 1 (a) Formulate the nonpreemptive goal programming model for this scenario. (Con- tinuous variables are acceptable.) (b) Solve your model using MATLAB (or other software). Summarize how much is shipped from each warehouse to each customer. Which goals are not met? 2. (Continuation of previous problem.) Consider the same problem using goal attainment. (a) Formulate a goal attainment problem for this scenario. (Continuous variables are acceptable.) (b) Solve your model using MATLAB (or other software). Summarize how much is shipped from each warehouse to each customer. Which goals are not met?