Answer: I applaud your desire to green up up your space and have beautiful color in your planter! Drip systems make watering easier because they're automatic; generally set on a timer to water at times you select. However, the water source must be constant - something I don't see possible without having a hose going out a window or door from your laundry area. An option might be to set up sprinklers in the lawn and planter area with a hose connected directly to the pipe and then coiled up when not in use. When it's time to water you could connect the hose to the spigot in the laundry area and turn it on. A second option would be to simply use a hose and sprinkler, without putting in any underground pipes. I think I'd vote for that option. Such a small area might take all of 15 minutes to hand water, and it would give you an excuse/reason for being outdoors, and an opportunity to amire and enjoy your lawn and flower bed. You might want to rethink the lawn - it will need mowing, but is too narrow for a lawn mower. How about planting a flowering groundcover instead? Natal plum (Carissa macrocarpa 'Green Carpet') is deep green and relatively low-growing, and it doesn't need mowing.
Best wishes with your new garden project!
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