Chapter 2.5, Problem 59E

College Admissions A university admissions committee anticipates an enrollment of 8000 students in its freshman class next year. To satisfy admission quotas, incoming students have been categorized according to their sex and place of residence. The number of students in each category is given by the matrix

$\begin{array}{l}\text{Male}\text{Female}\\ A=\begin{array}{c}\text{In-state}\\ \text{Out-of-state}\\ \text{Foriegn}\end{array}\left[\begin{array}{cc}2700& 3000\\ 800& 700\\ 500& 300\end{array}\right]\end{array}$

By using data accumulated in previous years, the admissions committee has determined that these students will elect to enter the College of Letters and Science, the College of Fine Arts, the School of Business Administration, and the school of engineering according to the percent ages that appear in the following matrix.

$\begin{array}{l}\text{L}\text{.\&S}\text{.}\text{Fine}\text{Arts}\text{Bus}\text{.}\text{Ad}\text{.}\text{Eng}.\\ B=\begin{array}{c}\text{Male}\\ \text{Female}\end{array}\left[\begin{array}{cccc}0.25& 0.20& 0.30& 0.25\\ 0.30& 0.35& 0.25& 0.10\end{array}\right]\end{array}$

Find the matrix $AB$ that show that number of In-state, Out-of-state, and foreign state students expected to enter each discipline.