They decided that a new policy is required for the inventory management for two reasons: (1) to keep the pace of the market and also not create a bad reputation for the company, and (2)to efficiently utilize the inventory’s space by having items that are required for production. This way the customers would obtain the cars that they require. Lagertha proposed to use the Pareto principle, and focus on keeping enough inventory to satisfy at least 80% of the customer orders. Then, Ragnar would need to identify the items required to stock to satisfy the greatest number of orders. After a comprehensive analysis, Lagertha and Ragnar decided that 20 cars are the models that the customers buy the most. These models have eight main components, divided into different styles, shown in the tables below:

Lagertha then created a table showing the 20 cars and the particular components for each of them. This is shown in the following table. The code at the top of the table corresponds to the eight components. For example, car model 1 requires floor type F2, seat type S2, multimedia type M4, security type A2, motor type G4, roof type R2, cameras type C2, and tires type T2.

Ragnar knew they had only a limited amount of warehouse space, such that they can hold 50square feet of floor, 12 seats, 2 types of multimedia equipment, 2 types of security equipment,3 types of motors, and 2 types of roofs. A combined total of 4 types of camera sets and/or tires sets can be allocated. Every car always includes exactly 20 square feet of floor and exactly five seats. Therefore,20 square feet of a particular style of floor and five seats of a particular style are required to be in stock.

1. Utilize BIP to maximize the total number of car models (and thus the number of customer orders) Drof stocks in the local warehouse. Assume that when a customer orders a car, all the particular components are replenished immediately (25 points).

Floor type (F1) Gray fabric (F2) White fabric (F3) Red fabric (F4) Blue fabric Motor (GI) Gas (G2) Hybrid Seats (S1) Black fabric (S2) Red fabric (S3) Black leather (S4) Red leather (G3) Plug-in hybrid (G4) Electric Multimedia Roof (RI) Metal roof (R2) Sunroof (MI) Basic (AI) Basic (M2) Touchscreen (A2) Lane keep assist (M3) Navigation (A3) Efficient cruise control (M4) Smartphone integration (A4) Lane keep and cruise control Cameras (CI) Reverse camera (C2) Reverse and front cam- Security era Tires (TI) 18" Basic (T2) 17" Basic (C3) Reverse camera with (T3) 18" Alu- proximity sensor minum (C4) Reverse and front cam- (T4) 17" Alu- era with proximity sensor minum