You’re thinking too far down the line. The article mentions this but its worth repeating: even the people producing and selling food don’t have access to refrigeration so a lot of the food they have spoils and goes to waste. That’s the first thing that needs to change. After that better roads and transport networks would help even more. Those things can at least get them out of food poverty and will also have second order effects that will increase economic output and put more money into people’s pockets.

Household appliances come much later after you’ve established a working economy and infrastructure.

Is it economically possible to make these investments?

Something makes me think when you're this poor - investing in better roads isn't viable.

For one, wouldn't rail be way more efficient?

Check out the railways that currently exist in Africa and the ones that were built by China and get back to me on that.