Question 1

Paper 1Medium5 marks

A shop records the weekly sales of two products. The sales are shown in Figure 1. The selling prices remain constant: product A costs $4.80 per unit and product B costs $6.25 per unit.

Week 1Week 2Week 302468101214161820222426283032WeekUnits sold● Product A (solid)□ Product B (dashed)
(a)

Write down the 2×32\times3 matrix SS of weekly sales, with rows corresponding to products A and B, in that order, and columns corresponding to Weeks 1, 2 and 3, in that order.

[2]
(b)

Let p=[4.806.25]\mathbf p=\begin{bmatrix}4.80&6.25\end{bmatrix} the row matrix of prices in dollars per unit.

Using your matrix from part (a), show that the revenue in Weeks 1, 2 and 3 is given by

pS=[215.20219.00261.40].\mathbf pS=\begin{bmatrix}215.20&219.00&261.40\end{bmatrix}.
[2]
(c)

Hence, state the week with the greatest revenue.

[1]

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