You are a Management Scientist hired to provide advice to a shipping company that has an existing contract to transport 280K products per month for Australia Post. The shipping company has already agreed to a certain price and has taken the following actions: It has hired 35 drivers on long term contracts and fixed salaries. It has signed a binding contract to purchase 50K litres of petrol every month at a fixed price. It has signed a binding contract with a local workshop that will provide the company with up to 400 hours of maintenance for its trucks, for a fixed monthly price. The contract with Australia Post states the following: the shipping company must transport all 280K or sub-contract the delivery of some products to other shipping companies. After careful negotiations with other shipping companies, you reach an agreement that subcontracting will cost you: $1/product for the first 25K products; $1.3/product for the next 25K products; and $1.6 for any additional products beyond the first 50K. To address the possible shortage of drivers you contact a recruitment firm that is able to hire up to 10 additional drivers for you at a cost of $8K per driver per month. Another concern the company has addressed is the uncertainty regarding the amount of petrol it will require every month. Thus, it has signed a contract with a local fuel supplier to purchase up to 10K additional litres of petrol at $1.5/litre or to sell excess amounts of petrol at $ 1.1/litre for up to 10K litres. The shipping company has not been able to address the uncertainty regarding the available hours of maintenance for its fleet of trucks. Hence, it cannot use more than 400 hours of maintenance and any unused resource is lost. The shipping company can operate four different types of trucks: models A, B, C and D. The monthly delivery capacity (the number of products it can deliver), driver requirements, maintenance (hours of maintenance required), and fuel consumption (the amount of petrol it will need every month) of the four models is given in the table below: MONTHLY MONTHLY DELIVERY MONTHLY HOURS OF TRUCK DRIVERS CAPACITY LITRES OF MAINTENA MODEL REQUIRED (NUMBER PETROL NCE OF REQUIRED REQUIRED PRODUCTS) A 2 11K 20 2000 B 2 9K 14 1700 1 7K 12 1200 D 1 6K 10 1100 You have been tasked with determining the number of trucks of each model the company should operate. In addition, you are required to determine the appropriate use of resources and a subcontracting policy. 1. Formulate a MILP model to solve the problem. 2. Solve the problem using Python (provide your code). 3. What is the optimal purchasing policy and what is the cost under this policy? (ignore the sunk costs, i.e., the cost of the existing resources). Provide a detailed discussion on the company's use of resources and the factors affecting the chose purchasing policy. You are a Management Scientist hired to provide advice to a shipping company that has an existing contract to transport 280K products per month for Australia Post. The shipping company has already agreed to a certain price and has taken the following actions: It has hired 35 drivers on long term contracts and fixed salaries. It has signed a binding contract to purchase 50K litres of petrol every month at a fixed price. It has signed a binding contract with a local workshop that will provide the company with up to 400 hours of maintenance for its trucks, for a fixed monthly price. The contract with Australia Post states the following: the shipping company must transport all 280K or sub-contract the delivery of some products to other shipping companies. After careful negotiations with other shipping companies, you reach an agreement that subcontracting will cost you: $1/product for the first 25K products; $1.3/product for the next 25K products; and $1.6 for any additional products beyond the first 50K. To address the possible shortage of drivers you contact a recruitment firm that is able to hire up to 10 additional drivers for you at a cost of $8K per driver per month. Another concern the company has addressed is the uncertainty regarding the amount of petrol it will require every month. Thus, it has signed a contract with a local fuel supplier to purchase up to 10K additional litres of petrol at $1.5/litre or to sell excess amounts of petrol at $ 1.1/litre for up to 10K litres. The shipping company has not been able to address the uncertainty regarding the available hours of maintenance for its fleet of trucks. Hence, it cannot use more than 400 hours of maintenance and any unused resource is lost. The shipping company can operate four different types of trucks: models A, B, C and D. The monthly delivery capacity (the number of products it can deliver), driver requirements, maintenance (hours of maintenance required), and fuel consumption (the amount of petrol it will need every month) of the four models is given in the table below: MONTHLY MONTHLY DELIVERY MONTHLY HOURS OF TRUCK DRIVERS CAPACITY LITRES OF MAINTENA MODEL REQUIRED (NUMBER PETROL NCE OF REQUIRED REQUIRED PRODUCTS) A 2 11K 20 2000 B 2 9K 14 1700 1 7K 12 1200 D 1 6K 10 1100 You have been tasked with determining the number of trucks of each model the company should operate. In addition, you are required to determine the appropriate use of resources and a subcontracting policy. 1. Formulate a MILP model to solve the problem. 2. Solve the problem using Python (provide your code). 3. What is the optimal purchasing policy and what is the cost under this policy? (ignore the sunk costs, i.e., the cost of the existing resources). Provide a detailed discussion on the company's use of resources and the factors affecting the chose purchasing policy