Question:

In Islandia, a small economy, Jack and Jill shall make their production and consumption decisions together. Jack can produce either 10 kg of banana or 14 kg of tea per day. Jill can produce either 8 kg of banana or 20.8 kg of tea per day. Suppose now they are open to trade with the rest of the world. The price of bananas is $$2/kg, and the price of tea is$$1/kg in the world market. Suppose Islandia is small enough that its behavior will not affect the world prices.

Jack and Jill will produce a total of [Answer] kg of bananas per day.

Below is my attempt:

First, I calculated the opportunity cost, and I got Jcak has a comparative advantage at producing bananas, and Jill has a comparative advantage at producing tea.

Then, I drew a diagram with banana as the X-axis and tea as the Y-axis. After putting the points (10,0),(0,14), (8,0),(0,20.8) into the equation. The function for Jack is y=-1.4x+14, and Jill's is y=-2.6x+20.8.

After that, I combined them together to get the new curves, which are y=-1.4x+25.2 and y=-2.6x+34.8, and the point of intersection is (8,14).

So, I put the price of bananas and tea into (8,14), (18,0), and (0,34.8). The maximum income is 18*2=36, so I thought the answer should be 18kg of bananas, but I was wrong.

I am confused about why I was wrong. I know this is a simple question, but I just cannot figure it out. So, could someone please help me out?