Quantitative Business Analysis
1. True/False: For each of the problem, state whether it is true or false.
a. Fixed cost problem is a common example of mixed integer programming.
b. Mutually exclusive constraints require both variables to be included or excluded at the
same time.
c. A multiple choice constraint involves selecting k out of n alternatives where k ≥ 2.
d. Mixed integer problems are harder to solve than the general linear programming problems
with continuous variables.
2. Stacey is forming a team to develop a new product for her company. To ensure that her team
incorporates a diverse range of viewpoints, she has been allowed to select team members from
across three departments. After speaking with several other managers, Stacey has identified 10
potential team members:
The Commitment score for each person is Stacey’s estimate, on a scale of 1-10, of how committed
the person would be to the project. The “Years” column shows how many years of experience the
person has.
Using the three steps, formulate an optimization model using binary decision variables to help
Stacey form a team that will maximize the total commitment level subject to the follow constraints:
x The team must have exactly five members.
x The team must have at least one member from each of the three departments (Marketing,
Engineering, and Accounting).
x The average of the number of years of experience of the team members must be at least 6.
x The team must have at least two women.
x The team must have at least two men.
x If Jing is chosen for the team, Guillaume must also be chosen.
x Bernie and Hilda can’t both be chosen.
x Alvin and Drew must either both be chosen or both left off.
3. The office manager of a large New York City-based accounting firm needs to replace the aging and
out-of-style office furniture in their New York offices. The firm has decided to purchase
desk/chair/credenza furniture sets for all 2,000 offices in New York. The company has received bids
from four different furniture companies who are willing to supply the furniture sets, as follows:
Carolina Woodworks has bid to deliver up to 1,000 furniture sets at a cost of $2,500 per set and
with a one-time charge of $10,000.
Nashawtuc Millworks has bid to deliver up to 1,200 furniture sets at a cost of $2,450 per set and
with a one-time charge of $20,000.
Adirondack Furnishing Designs has bid to deliver up to 800 furniture sets at a cost of $2,510 per set
with no additional charges.
Lancaster Artisan Company has bid to deliver up to 1,100 furniture sets at a cost of $2,470 per set
and with a one-time charge of $13,000.
a) Formulate a mixed integer optimization model that could be used to determine how many
furniture sets to purchase from each of the four potential suppliers in order to minimize cost.
Make sure to follow the three steps clearly.
b) Use Excel to find the optimal solution. Turn in your spreadsheet.
c) In your Word/ PDF file, report how many furniture sets to order from each supplier.
d) In your Word/ PDF file, report what the total cost will be.
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