ABC Company can produce 4 types of tires. Each tire needs to be processed on two machines. The profit it obtains from each type of tire and the number of hours required on each machine is shown below. (hand in your LINGO code and output including range analysis). Tire 1 Tire 2 Tire 3 Tire 4 Hours available Machine 1 0.02 0.03 0.05 0.04 40 Machine 2 0.05 0.02 0.04 0.04 50 Profit $50 $40 $85 $35 (a) Formulate a LP model to determine how many of each type of tire ABC should product to maximize profits. Code and solve model using LINGO. What is the profit from tire 3? (5 + 1 = 6 marks) (b) Are there any unused machine 1 hours? machine 2 hours? (2 mark) (c) How much will profit increase by for each additional hour available on machine 2? For what range of machine 2 hours is this valid? (1 + 2 = 3 marks) (d) Currently, the profit for each tire 3 is $85. How much can profit for each tire 3 increase to and still have the same number of tires produced in (a)? (2 marks)