4. Orrin Sage is opening a bicycle shop and considering his initial order of bicycles for the coming season. Orrin is considering two different suppliers of bikesHoosier Bikes and Albatross Imports. With either supplier, there will be costs associated with setting up the contract. He estimates this cost of being $5,000 with Hoosier Bikes and $6,000 with Albatross Imports. His entire budget for purchasing bikes is $50,000 (including cost of contracts). a. Formulate a linear program to help him maximize his profits. Use the following decision variables: fori=H,A,andj=K,M,C,R, xij : number bikes purchased from supplier i of type j; yi binary variable of supplier i; i.e., yi=1 if Orrin signs a contract with Supplier i;yi=0, otherwise. b. Albatross Imports has a special incentive for retailers who sign up to only sell their bikes. If Orrin buys only from them, they will give a rebate of $3,000 at the end of the year on his order. Modify your model from part a. (You may need to add a variable.) c. Hoosier Bikes are in great demand and the supply is limited for retailers who are not designated as a Hoosier Bikes' Exclusive Dealer. For this year Hoosier Bikes has a limit of 75 of each type of bike for retailers who are not Exclusive Dealers. If Orrin signs up be a Hoosier Bikes' Exclusive Dealer and only buy bikes from them (and none from Albatross), they will supply all of his demand. Modify your model from part a