The dean the Western College of Business must plan the school%u2019s course offe

Question

The dean the Western College of Business must plan the school%u2019s course offerings for the fall semester. Student demands make it necessary to offer at least 30 undergraduate and 20 graduate courses in the term. Faculty contracts also dictate that at least 60 courses be offered in total. Each undergraduate course taught costs the college an average of $2,500 in faculty wages, and each graduate course costs $3,000. How many undergraduate and graduate courses should be taught in the fall so that total faculty salaries are kept to a minimum?

Explanation / Answer

Let X1 = the number of undergraduate courses scheduled X2 = the number of graduate courses scheduled Minimize 2,500X1 + 3,000X2 (minimize faculty salaries) Subject to: X1 ? 30 (schedule at least 30 undergrad courses) X2 ? 20 (schedule at least 20 grad courses) X1 + X2 ? 60 (schedule at least 60 total courses) X1, X2 ? 0 (non-negativity constraints) Optimal Solution: X1 = 40 X2 = 20 Cost = $160,000

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