Mr Faizal stays in a terrace house in the east of Singapore. He is considering installing solar panel at his home. He wants to know if the cost of installing the solar panel can offset the cost of his electricity bill. He did some research and gets a quotation from a company that installs solar panel. Based on his house type, he is recommended to use the 60-cells solar panel.

1. Identify how many 60-cell panels fit in the more efficient orientation.

For a 60-cell solar panel, the dimensions are approximately $1.0\text{ m} \times 1.65\text{ m}$.

Place the $1.65\text{ m}$ side along the $9\text{ m}$ side of the roof:

$\left\lfloor \frac{9}{1.65} \right\rfloor = 5$

Place the $1.0\text{ m}$ side along the $4\text{ m}$ side of the roof:

$\left\lfloor \frac{4}{1.0} \right\rfloor = 4$

2. Calculate the maximum number of panels and check against the alternative simple orientation.

Number of panels in this arrangement:

$5 \times 4 = 20$

If placed the other way round:

$\left\lfloor \frac{9}{1.0} \right\rfloor \times \left\lfloor \frac{4}{1.65} \right\rfloor = 9 \times 2 = 18$

Hence the maximum number is $20$.