A shop sets each of its two branches a weekly sales target, the same every week. The matrix T shows

Question

A shop sets each of its two branches a weekly sales target, the same every week. The matrix $T$ shows the weekly targets and the matrix $M$ shows the numbers actually sold in the 4 weeks from 1 to 28 April.

$T=\begin{pmatrix}40&15\\ 30&12\end{pmatrix}\qquad M=\begin{pmatrix}172&54\\ 115&50\end{pmatrix}$

In both matrices the rows are Branch X, Branch Y and the columns are phones, tablets.

Evaluate $4T$.[1]
Evaluate $D=M-4T$.[2]
Explain what the two entries in row 1 of $D$ represent.[2]
Explain why $M-T$ is not a useful comparison.[1]

Accepted Answer

(a) $\begin{pmatrix}160&60\ 120&48\end{pmatrix}$ (b) $\begin{pmatrix}12&-6\ -5&2\end{pmatrix}$ (c) Branch X sold 12 phones more and 6 tablets fewer than its target for the 4 weeks (d) T is for one week and M is for four weeks, so the entries do not cover the same period

Sales against weekly targets

Sales against weekly targets

Solution:

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