A banner needs to be enlarged from its original format. The dimensions of the original are 4 cm tall by 25cm wide. The enlarged banner needs to be at least 8 m wide but no more than 1.4 m tall. Calculate the minimum and maximum ratios of enlargement possible.

To find the minimum and maximum ratios of enlargement, we need to compare the dimensions of the original banner to the desired dimensions of the enlarged banner.

Let's start with the minimum ratio of enlargement. The width of the original banner is 25 cm, and it needs to be enlarged to at least 8 m (800 cm). To find the minimum ratio, we'll divide the desired width of the enlarged banner by the original width:

Minimum Ratio = Desired Width / Original Width
Minimum Ratio = 800 cm / 25 cm
Minimum Ratio = 32

So, the minimum ratio of enlargement is 32.

Next, let's find the maximum ratio of enlargement. The height of the original banner is 4 cm, and it should not exceed 1.4 m (140 cm) in height. To find the maximum ratio, we'll divide the desired height of the enlarged banner by the original height:

Maximum Ratio = Desired Height / Original Height
Maximum Ratio = 140 cm / 4 cm
Maximum Ratio = 35

Therefore, the maximum ratio of enlargement is 35.

In summary, the minimum ratio of enlargement is 32, and the maximum ratio of enlargement is 35.