Question

The VP of admissions has a second concern as well.  There are variety of ways to attract students and increase applications.  The university can purchase online advertising, send out traditional mailings, and do in-person recruiting at various functions.  The VP estimates that each online ad will result in 50 new applications, each traditional mailing will result in 30 new applications, and each recruiting event will result in 12 new applications. Online advertising costs $800 per ad, mailings cost $600 each, and in-person recruiting events are quite inexpensive at $150 per appearance.   The university wants to maintain a broad presence, so at least 2 of each form of recruiting is desired.  There are limited personnel available for recruiting, so a maximum of 5 in-person recruiting events can be managed.   At least half of the advertising must be online, as the university president wants to expand enrollments in on-line programs.  The VP has a budget of $8,000.  The VP wants to understand the mathematical problem that must be solved to figure out how many of each type of advertising should be used, and have an Excel file that can solve the problem.  (For convenience, feel free to solve the problem in terms of partial units…i.e. the final answer can be 1.2 online ads, 2.6 mailings, etc.).  How many of each form of outreach should be purchased?

Answer 1

Decision Variables:

Let,

The number of online ads = x1

Traditional mailing = x2

In-person recruitment = x3

Objective Function:

The objective of the VP, Admissions is to maximize the number of new applications.

Each online ad results in 50 new applications

Each traditional mailing results in 30 new applications

Each in-person recruitment results in 12 new applications.

Hence, the objective function is:

MAXIMIZE 50*x1 + 30*x2 + 12*x3

Constraints:

The VP has a budget of $8,000. He/she cant exceed the budget in terms of spending.

Each online ad costs $800

Each traditional mailing costs $600

Each in-person recruitment costs $150.

800*x1 + 600*x2 + 150*x3 <= 8000

A broad presence is expected. Hence at least two of each type is desired.

x1 >= 2

x2 >= 2

x3 >= 2

Limited personnel available for in-person recruitment results in maximum 5 in-person recruiting events.

x3 <= 5

At least half of the advertising should be online.

x1 >= 0.5*(x1 + x2 + x3)

0.5*x1 – 0.5*x2 – 0.5*x3 >= 0

So the mathematical model is:

Decision Variables:

The number of online ads = x1

Traditional mailing = x2

In-person recruitment = x3

Objective Function:

MAXIMIZE 50*x1 + 30*x2 + 12*x3

Constraints:

800*x1 + 600*x2 + 150*x3 <= 8000

x1 >= 2

x2 >= 2

x3 >= 2

x3 <= 5

0.5*x1 – 0.5*x2 – 0.5*x3 >= 0

Modeling into Excel:

Solver Parameters:

Optimal Solution:

As we can leave answer in fraction (as per the requirement in the question):

Online Ads	Traditional Mailing	In-Person Recruitment
x1	x2	x3
7.5625	2	5

Number of Online Ads = 7.5625

Traditional Mailing = 2

In-Person Recruitment = 5

Maximum number of applications: 498.125

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