Quantitative Methods

Quantitative Methods: UGBS 301

Assignment 2

Instructions: This assignment is due on or before 21/09/2015 at 11:59 pm. All

responses are to be typed nicely in MS word and submitted through your drop box

in Sakai. Spreadsheet modelling and Solver Output for Q3 and Q4 are also to be

attached to solutions.

1. A school is preparing a trip for 400 students. The company who is providing the transportation

has 10 buses of 50 seats each and 8 buses of 40 seats, but only has 9 drivers available. The rental

cost for a large bus is $800 and $600 for the small bus. Formulate this as a linear programming

problem and solve using the graphical method to determine the mix of buses that leads to the least

possible cost for the trip. Clearly state the decision variables and show step by step your approach.

2. A youth camp organizing company has received 800 applications for the upcoming summer

camp. The company has 10 buses of 50 seats each and 8 buses of 40 seats, but has only 15 drivers

available. Each 50 seater and 40 seater bus will bring in a profit of $800 and $700 respectively. A

50 seater bus would require 40 gallons of fuel for the trip, whiles a 40 seater bus would require 30

gallons for the trip. The company can only afford 600 gallons of fuel for the upcoming trip.

Formulate this as a linear programming problem and solve using the simplex method to determine

the mix of buses that will generate maximize profit from the youth camp. Clearly state the decision

variables and show step by step your approach for the simplex method. From your solution, what

are the values of your decision variables as well as the objective function?

3. Adirondack Savings Bank (ASB) has $1 million in new funds that must be allocated to home

loans, personal loans, and automobile loans. The annual rates of return for the three types of loans

are 7% for home loans, 12% for personal loans, and 9% for automobile loans. The bank’s planning

committee has decided that at least 40% of the new funds must...