To graduate from Kale University with a major in operations research, a student
ID: 3123627 • Letter: T
Question
To graduate from Kale University with a major in operations research, a student must complete at least two math courses, and at least two OR courses, and at least two computer courses. Some courses can be used to fulfill more than one requirement: "Calculus" and "Linear Algebra" can fulfill math requirement, "Linear Programming" can fulfill math and OR requirements, "Data Structures" can fulfill computer and math requirements; "Simulation" can fulfill computer and OR requirements, "Statistics" can fulfill math and OR requirements, "Computer Programming" can fulfill computer requirement, and "Stochastic Processes" can fulfill math and OR requirements. Some courses are prerequisites of others: Calculus is a prerequisite of Statistics and Linear Algebra, Linear Algebra is a prerequisite of Linear Programming, Computer Programming is a prerequisite of Simulation and Data Structures. Statistics is a prerequisite of "Stochastic Processes." Formulate an IP that minimizes the number of courses needed to satisfy the major requirements.Explanation / Answer
M - Maths, C - Computer
The total requirement (T) to pass the course can therefore be expressed as-
T = M + C + OR
Now, we have to minimize T subject to following conditions-
M >= 2 (atleast 2 courses)
OR >= 2
C >= 2
Cal = M, La = M, Cp = C
Lp = M + OR Ds = C + M Sp = M + OR Si = C + OR St = M + OR
Cal - Calculus, La - Linear algebra, Cp - Computer programming, Lp - Linear programming, Ds - Data structures,
Sp - Stochastic processes, Si - Simulation, St - Statistics
The above eqautions specify the subject requirement that is fulfilled when a specific course is chosen.
The prerequisite order can be specified as below. The > sign indicates that quantity on the left side is a prerequisite for the one on the right side -
Cal > St
Cal > La
La > Lp
Cp > Si + Ds
St > Sp
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