[3 points] This year, a US-based MBA program, famous for its high tuition fee ($55,500 per year), has received many applications. The admission officials need to decide how many admission letters to send out. Based on professors and the management’s consensus, the ideal class size is 180.

If the class size were above the ideal level, the resultant mismatch between the available resources and students’ requirements would lead to a loss of the business school’s long- term reputation. A well-respected economics professor in the business school estimated that an “extra” student would bring the school a reputational loss of $185,000.

The admissions officials further learned that the number of applicants who reject their offers is normally distributed, with a mean of 100, and a standard deviation of 50.

Assume that the MBA program takes two years and the tuition is frozen in the next two years. The cost for providing the education does not depend on the number of enrolled students. Please help the admission officials decide on the number of admission letters to send out.

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