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The Dean of Physical and Mathematical Sciences of ABX University is drawing up her plan for the full time professor needs for the next four years. After looking at the projected total credit hours offered in each year, she finds out that the required number of professors should be:
Year 2020 2021 2022 2023
no. of Profs required 72 94 69 103
From past experience, she knows that professors prefer long term job contracts and that they would accept a lower salary if the contract is longer. The table below displays professorial salaries based on contract length.
Length of Contract in yrs: 1 2 3 4
Salary in £000's 120 110 100 90
For example, if a professor is needed for two years, it is better to sign a two year contract and pay £220,000 over the duration of the appointment, instead of £240,000 for two one-year contracts. Suppose that the Dean is starting afresh, that is no contracts exist with any professor.
Formulate a linear program to minimise the total salaries paid to professors at this Faculty while ensuring that there are enough professors signed up for each year. Clearly state the decision variables, the objective function and all the constraints.
I am confused with this because I'm not too sure on what the correct variables are and what the objective function and the constraints for this question.
