Matrices - Application of Matrices

The table below shows the number of cups of yoghurt of two flavours: Peach and Mango, sold at three dessert shops in March and April.

The information for the selling price of yoghurt in the three shops can be represented by the matrix \(P = \begin{pmatrix} 3.5 & 3.2 & 4 \end{pmatrix}\). The information for the number of cups of yoghurt sold in March can be represented by the matrix \(Q = \begin{pmatrix} 200 & 330 \\ 250 & 430 \\ 160 & 220 \end{pmatrix}\).

1. Write down a \(3 \times 2\) matrix \(R\) to represent the number of cups of yoghurt sold in April.
2. Given that \(T = Q + R\), evaluate \(T\).
3. Explain what the elements in \(T\) represent.
4. Given that \(N = PT\), evaluate \(N\).
5. Explain what the elements in \(N\) represent.
6. During a promotion, the amount of sales for Peach yoghurt increased by \(30\%\) and the amount of sales for Mango yoghurt increased by \(20\%\). Write down a matrix such that its product with \(N\) gives the total amount of sales for each type of yoghurt during the promotion. Evaluate the product.
7. Using matrix multiplication, find the total amount of sales for the three shops during the promotion.