Question 4. (Integer programming formulation Orrin Sage is opening a bicycle shop and considering his initial order of bicycles for the coming season. Orin is considering two different suppliers of bikes - Hoosier 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 .) Bike Costs (per bike ) Kids (K) Mountain (M) Comfort (C) Road (R) Hoosier Bikes (H 45 110 100 400 Albatross Imports (A) 30 130 90 475 Selling Price 90 24 190 700 Projected Demand 60 100 80 60 a. Formulate a linear program to help him maximize his profits Use the following decision variables : for i = H, A, and j = K, M, C, R, x, : number bikes purchased from supplier i of type j; y: binary variable of supplier i; i.e. y. = 1 if Orrin signs a contract with Supplier i; y, = 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 $3000 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 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. Question 5. (Simulation modeling ) W.L. Linderoth, a direct marketer of women's clothing , must determine how many telephone operators to schedule during each part of the day . W.L. Linderoth estimates that the number of phone calls received each hour of a typical 8-hour shift can be described by the probability distribution : probability 10% 40% 30 % 15% 5% # of calls 80 120 160 200 300 Each operator can handle 15 calls per hour and costs the company $20 per hour . Each phone call that is not handled is assumed to cost the company $6 in lost profit . Considering the options of employing 6. 8, 10, 12, 14, or 16 operators , use simulation to determine the number of operators that minimizes the expected hourly cost (labor costs plus lost profits ). Build a simulation model on Excel sheet , run simulation with 800 random samples , use data table to find the best number of operators to employ