Question

The Cinema Center consists of four theaters: Cinemas I, II, III, and IV. The admission price for one feature at the Center is $5 for children, $7 for students, and $9 for adults. The attendance for the Sunday matinee is given by the matrixChildren - Students - AdultsCinema I - 225 - 110 - 70Cinema II - 95 - 160 - 225Cinema III - 280 - 65 - 110Cinema IV - 0 - 240 - 225a. Write a column vector B representing the admission prices.b. Compute AB, the column vector showing the gross receipts for each theater.c. Find the total revenue collected at the Cinema Center for admission that Sunday afternoon.

Answer 1

a) Matrix B =
`\left[\begin{array}{c}5\\7\\9\end{array}\right]`

b) Matrix AB =
`\left[\begin{array}{c}2525\\3620\\2845\\3705\end{array}\right]`

c) $12,695

Explanation:

Matrix A =
`\left[\begin{array}{ccc}225&110&70\\95&160&225\\280&65&110\\0&240&225\end{array}\right]`

a) Matrix B =
`\left[\begin{array}{c}5\\7\\9\end{array}\right]`

Gross Receipt = AB

`\left[\begin{array}{ccc}225&110&70\\95&160&225\\280&65&110\\0&240&225\end{array}\right]` .
`\left[\begin{array}{c}5\\7\\9\end{array}\right]` =
`\left[\begin{array}{c}2525\\3620\\2845\\3705\end{array}\right]`

c) Total revenue is the sum of receipts from 4 cinemas given in part b

Hence,

Total revenue = $2525 + $3620 + $2845 + $3705 = $12,695