Business Statistics and Research Methods – ISM 2016
Final Assignment
1. During the seminar we worked with the following cases:
a. Color chips
b. Computers S and P
c. Make or buy – Hamlet Inc.
d. Reallocating bikes
e. Assigning planes
Describe briefly (not more than five lines per case) the main lessons that you got from each one of these cases.
2. Explain with several practical examples why sensitivity analyses (objective function coefficients and RHS constraints) are so important.
3. Let’s suppose that two constraints have the following shadow prices:
Constraint A = 612.35
Constraint B = 25.00
Is it obvious that multiplying by two the constraint A’s RHS is more interesting that multiplying by two the constraint’s B RHS?
4. In the next page you will find the case about public health that I handled to you at the end of the seminar. Develop the optimization model, find the numerical solution using Excel and comment your results.
5. Talking about central tendencies, in which cases the median and the mode can be more useful than the mean? Illustrate through real life examples.
6. Construct two series (A and B) of 20 non-negative values each with the following characteristics:
a. Means not differing more than 1%
b. Mode of series B approximately four times mode of series A
c. Standard deviation of series A approximately eight times more than standard deviation of series B
7. Explain why it is so important to consider the seasonal factors when doing forecasting.
8. Which were the main lessons you got from the practical exercise about IESA grades?
Question 1 worths 5 points. Other questions worth 8 points
Remember that this final assignment is strictly individual
INTERNATIONAL SCHOOL OF MANAGEMENT
BUSINESS STATISTICS AND RESEARCH METHODS
February 2016
A case about public health
You are the administrator of your state’s Public Health Department. You must decide how to allocate a special fund among the five counties of your state. The fund will be used to provide scholarships to three kinds of individuals: pregnant women, babies (less than 1 year old) and children (1 to 4 years old). You should achieve the following goals:
a. Each one of the five counties should receive, at least, 10% of the total fund.
b. Counties 3 and 4 (the poorest ones) should receive, at least, 50% of the fund.
c. Counties 1, 2 and 3 (the most populated ones) should receive, at least, 75% of the total fund.
d. The minimal number of pregnant women, babies and children that should receive a scholarship is shown in Table I.
Table I – Minimal total number of scholarships per category of individuals
Table II – Number of scholarships provided per 1000 euros of allocated funds
Table II shows the number of scholarships for women, infants and children that each county will allocate for every 1000 euros received. Thus, if county 3 receives 400,000 euros, this county will allocate:
400 * 0.5 = 200 scholarships for pregnant women
400 * 1.5 = 600 scholarships for babies
400 * 1.0 = 400 scholarships for children
Using your know-how in linear programming, find the minimal amount of the total fund and the optimal allocation to each county in order to meet the proposed goals.
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