How to get an equation, graph it, and solve it?

Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter2: Introduction To Spreadsheet Modeling
Section: Chapter Questions
Problem 20P: Julie James is opening a lemonade stand. She believes the fixed cost per week of running the stand...
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How to get an equation, graph it, and solve it?

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The Admissions Office at Big State University needs to decide how many in-state students
and how many out of state students to admit to the next class. Like many universities, Big
State U has limited resources, and budget considerations have to play a part in admissions
policy.
Here are the constraints on the Admissions Office decision:
The college president wants this class to contribute a total of at least $2,500,000 to the
school after it graduates. In the past, Big State U has gotten an average of $8,000 in
contributions from each in-state student admitted and an average of $2,000 from each out-
of-state student admitted.
The faculty at the college wants entering students with good grade point averages. Grades
of in-state students average less than grades of out-of-state students. Therefore, the faculty
is urging the school to admit at least as many out-of-statę students as in ștate- students.
The housing office is not able to spend more than $85,000 to cover costs such as meals and
utilities for students in residence halls during vacation periods. Because out-of-state
students are more likely to stay on campus during vacations, the housing office needs to
take these differences into account. In-State students will cost the office an average of $100
each for vacation-time expenses, while out of state students will cost an average of $200
each.
The college treasurer needs to minimize educational costs. Because students take different
courses, it costs an average of $7,200 a year to teach an in-state student and an average of
$6,000 a year to teach an out-of-state student.
Phew...
Your job is to recommend how many students from each category should be admitted to
Big State U. You need to minimize educational costs, as the treasurer requires, within the
constraints set by the college president, the faculty, and the housing office.
(our write up should include a proof that your solution is the best possible within the
Transcribed Image Text:Imi 12 13 14' 15 16 17 18 19 |6 10 11 20 ' 21' 22' 23 24' 25 18 71 6 50 41 31 The Admissions Office at Big State University needs to decide how many in-state students and how many out of state students to admit to the next class. Like many universities, Big State U has limited resources, and budget considerations have to play a part in admissions policy. Here are the constraints on the Admissions Office decision: The college president wants this class to contribute a total of at least $2,500,000 to the school after it graduates. In the past, Big State U has gotten an average of $8,000 in contributions from each in-state student admitted and an average of $2,000 from each out- of-state student admitted. The faculty at the college wants entering students with good grade point averages. Grades of in-state students average less than grades of out-of-state students. Therefore, the faculty is urging the school to admit at least as many out-of-statę students as in ștate- students. The housing office is not able to spend more than $85,000 to cover costs such as meals and utilities for students in residence halls during vacation periods. Because out-of-state students are more likely to stay on campus during vacations, the housing office needs to take these differences into account. In-State students will cost the office an average of $100 each for vacation-time expenses, while out of state students will cost an average of $200 each. The college treasurer needs to minimize educational costs. Because students take different courses, it costs an average of $7,200 a year to teach an in-state student and an average of $6,000 a year to teach an out-of-state student. Phew... Your job is to recommend how many students from each category should be admitted to Big State U. You need to minimize educational costs, as the treasurer requires, within the constraints set by the college president, the faculty, and the housing office. (our write up should include a proof that your solution is the best possible within the
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