A formal proposal shows that you take your work seriously. Write up the information you've collected about your job. Include information on what days you'd like to work from home, how you'll be available to your boss and coworkers, and how you plan to compensate for any tasks that are more difficult at home. Also, note how you plan to work the same (or similar) hours from home. When you go to talk to your boss, have the proposal in hand. You can say, "I'd like to talk to you about the possibility of telecommuting. I've written up a proposal about how I think this will work." Then you can lay out the basics of your proposal. Most of the time, your boss isn't going to care about how working from home will make you happier. Even if they do care, they care more about how productive you can be at home. Make it a point to show your boss that you believe you can actually be more productive at home, away from the distractions of coworkers. For example, you could say, "I know one of your concerns will be productivity. However, I actually believe I will be more productive at home. Sometimes in the office, the noise is a distraction. At home, that won't be a problem, and I can focus more effectively on my work." Your boss is likely going to have some questions, particularly if you are one of the first employees to suggest telecommuting. Take some time to figure out solutions for each problem. It's best to think through as many solutions as you can before talking to your boss. For example, if your boss is worried about accountability, offer a way to maintain accountability by having weekly meetings over video chat or even in-office. You could also offer to write up weekly reports. Talk to tech support to ensure you could have the same level of security that the office has, which will put your boss more at ease. Discuss any special accommodations, such as setting up a VPN and whether you'll need to get a work computer for home (if you don't already have one). It's best if you can get the agreement in writing. That way, if you get a new boss, you still have an agreement with the company to work from home. Even a set of emails will do in a pinch. " If your boss does end up saying "no," accept it, and plan to revisit the idea in the future. Getting upset or sulking isn't going to help your case any. If you prove you're a hard worker who can handle responsibility, your boss is more likely to be lenient in the future.
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One-sentence summary -- Create a formal proposal. Focus on how productive you can be. Address your boss's concerns. Get it in writing. Accept a "no.

You are now a week into the diet and will probably be tired and hungry. Day seven starts with no breakfast, just a cup of tea without sugar. It gets worse with no lunch, just lots and lots of water. You do get to eat something in the evening, but only 200 grams (7.1oz) of lamb and one apple. Day eight is a little easier, but you still go without breakfast and only drink a coffee with one sugar. Day eight is the same as day one: two hard boiled eggs with 400 grams (14oz) of boiled spinach and a tomato for lunch. In the evening you can eat 200 grams (7.1oz) of beef with 150 g (2 cups) of lettuce. You can add a little lemon juice and olive oil to the lettuce for extra flavour. On day nine you continue to skip breakfast, just drinking a coffee with one sugar. At lunch time you are permitted to eat 250 grams (8.8oz) of lean ham along with one pot of natural yoghurt. For dinner you can eat a little more than the previous evening: 250 grams (8.8oz) of beef with 150 g (2 cups) of lettuce. On day 10 you have one slice of bread with your coffee for breakfast, the first solid breakfast since day six. Lunch is two hard boiled eggs together with 100 grams (3.5oz) of ham and some lettuce on the side. The food for the evening the same as day three, just one tomato, some boiled celery and one serving of fruit. The end is almost in sight, and you will no doubt be feeling the strains of such a severely restrictive diet. On day 11 stick with a coffee and one slice of bread for breakfast. For lunch eat one pot of natural yoghurt and drink 200 milliliters (6.8floz) of orange juice. Day 11 is the same as day four and for dinner you again eat one hard boiled egg, one carrot and one serving of cottage cheese. On day 12, have just one carrot for breakfast, before eating 200 grams (7.1oz) of boiled fish for lunch. You can add a little butter and lemon juice to the fish. For your dinner eat 250 grams (8.8oz) of beef with some celery on the side. On the final day start with the familiar breakfast of one cup of coffee with a slice of toast. For lunch you can eat two hard boiled eggs along with one carrot. On the last day the diet advises you to skip the evening meal altogether.
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One-sentence summary --
Continue with days seven and eight. Keep going for days nine and 10. Push on to days 11 and 12. Finish on day 13.