2025 CCHY PRELIMS P2 Q5

Salim owns three cafes A, B and C which sell burgers and salad.
The cafes operate \(7\) days a week. The sales on a weekend are on average half of that on a weekday.

1. Suggest a reason why sales on a weekend are lower than sales on a weekday.

   [1]

The matrix \(\mathbf{F}\) shows the average number of food items that are sold on a weekday.

\(\begin{matrix} & \begin{matrix} \!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\! \text{Burger} & \text{Salad} \end{matrix} \\ \mathbf{F} = & \begin{pmatrix} 120 & 11 \\ 12 & 135 \\ 80 & 92 \end{pmatrix} \begin{matrix} \text{Cafe A} \\ \text{Cafe B} \\ \text{Cafe C} \end{matrix} \end{matrix}\)

2. Evaluate the matrix \(\mathbf{W}=6\mathbf{F}\).

   [1]

3. In all of his three cafes, each burger costs \(\$12\) and each plate of salad costs \(\$8\).

   Represent the costs of the food items in a \(2\times1\) column matrix \(\mathbf{C}\).

   [1]

4. Evaluate the matrix \(\mathbf{R}=\mathbf{WC}\).

   [2]

5. State what each of the elements of \(\mathbf{R}\) represents.

   [1]

6. All the food items are sold for \(40\%\) profit.

   By writing down a row matrix \(\mathbf{T}\), find \(\mathbf{TR}\) which gives the total amount of profit all three cafes made in a week.

   [2]