Management Science

QMT 2001 Management Science Homework #1 Due on October 31, 2014 Notes: This is not a group homework. Work alone. Also, please write your full name and student ID number on top-right corner of every page. 1) (40 pts) For the LPs listed below, - Graph the constraints and show the feasible region on the graph. (Write the equations on each line.) - Calculate the objective function value on each extreme (corner) point. State which one is optimal.

2) (30 pts) The MTA, an urban transit authority, is considering the purchase of additional buses to expand its service. Two different models are being considered. A small model would cost $100,000, carry 45 passengers, and operate at an average speed of 25 miles per hour over the existing bus routes. A larger model would cost $150,000, carry 55 passengers, and operate at an average speed of 30 miles per hour. The transit authority has $3,000,000 in its capital budget for purchasing new buses during the forthcoming year. However, the authority is also restricted in its expansion program by limitations imposed on its operating budget. Specifically, a hiring freeze is in effect and only 25 drivers are available for the foreseeable future to operate any new buses that are purchased. To plan for increased future demand, the transit authority wants at least one-half of all new buses purchased to be the larger model. Furthermore, certain bus routes require the use of the small model (because of narrow streets, traffic congestion, and so on), and there is an immediate need to replace at least five old buses with the new small model. The transit authority wishes to determine how many buses of each model to buy to maximize additional capacity measured in passenger-miles-per-hour while satisfying these constraints. Formulate the LP model. 3) (30 pts) Solve the following LP model using simplex method:

4) (Bonus Question – 20 pts) For Question 3, assume you don’t know the coefficient of x1 in the objective function (i.e. the objective...