0606 P21 - Jun 2017 - Q6 - 5 marks
8586
Four cinemas, \(P\), \(Q\), \(R\) and \(S\) each sell adult, student and child tickets. The number of tickets sold by each cinema on one weekday were
| Cinema | Adult | Student | Child |
|---|---|---|---|
| \(P\) | 90 | 10 | 30 |
| \(Q\) | 0 | 45 | 0 |
| \(R\) | 25 | 0 | 15 |
| \(S\) | 10 | 0 | 100 |
(i) Given that \(L=(1\ 1\ 1\ 1)\), construct a matrix \(M\), of the number of tickets sold, such that the matrix product \(LM\) can be found.
(ii) Find the matrix product \(LM\).
(iii) State what information is represented by the matrix product \(LM\).
An adult ticket costs \(\$5\), a student ticket costs \(\$4\) and a child ticket costs \(\$3\).
(iv) Construct a matrix \(N\), of the ticket costs, such that the matrix product \(LMN\) can be found and state what information is represented by the matrix product \(LMN\).
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