18. The dean of the Western College of Business must plan the school’s course of

Question

18. The dean of the Western College of Business must plan the school’s 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 Undergraduate courses be U

Let graduate courses be G

U + G >= 60

U >=30

G >= 60

Objective = minimize the salaries in total = 2500U+3000G

so the answer would be Since the graduate courses cost more, they should be kept at minimum possible

so G = 20

U = 60 - 20 = 40 (minimum total courses are 60 and only objective here is to minimize the salary as minimum)

total salary = 40*2500+3000*20=$160,000

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