This really depends on the stage you're at.
Keep in mind that I don't know your specific product or service, so I'm offering you some general advice. If you want to do a call I'd be happy to provide more tailored analysis.
Currently I run two businesses: BizeeBee (SaaS product), and Femgineer (education services). For both and in general, I never expected to make a profit off a customer in the early stages. I'm usually trying to figure out a customer's price sensitivity and price model (one-time purchase, subscription, contract, freemium, etc.).
Having said that in the beginning you can expect to make almost little to no profit off of a customer, because you're spending every penny on building awareness, capturing mindshare, and creating a high quality experience. The reason you're even asking them to pay is just to validate their "willingness to pay". I stay away from thinking of early customers are profitable once, and think more of them as my early evangelists. I want to create case studies off of them, and have them spread the word about my company.
You'll obviously want to set a budget, which it looks like you have for acquisition. But it's really hard to figure out the exact unit economics, mainly because you don't know how much it's going to go cost you yet to service them.
I say service them, because you might have attracted some customers at certain price point who are actually more demanding than you'd like, as a result your servicing costs maybe even greater than acquisition. So you'll want to track that to either avoid attracting those kinds of customers in the future, or possibly increase your price point to cover the cost of servicing customers.
Finally, the profitability of a customer depends on the type of product you have. If you have a one-time use product, then barring returns, you should be able to know the profitability pretty quickly after the sale i.e. expiration date of the return policy. If instead you are operating as an ongoing service then it's likely that it will take much much longer. If you're offering a service then you have to restate the value proposition every time someone is paying you i.e. monthly subscription or renewing a contract, and keep track of costs to servicing them during that period of time.