Which freelance project should you take? The hours math
Short answer: take the set of projects that earns the most from the hours you actually have, not the single biggest fee and not the best hourly rate. Hours can move between weeks, but a project's hours must be done by its deadline, so a set is deliverable only if, for every deadline, the hours due by then fit the hours you have by then.
A worked example
You have 30 billable hours a week, but only 15 in week 3. Offers: a $6,000 brand site (60 h, due week 3), a $2,400 landing page (40 h, week 2), a $3,200 dashboard (35 h, week 4), a $1,800 bug-fix month (12 h, week 1), a $5,200 app MVP (80 h, week 5), a $900 template (10 h, week 5) and a $2,600 audit (30 h, week 5).
Best hourly rate first starts with the bug-fix month ($150/h), which uses 12 early hours, and then the dashboard no longer fits before its week-4 deadline: it ends with the bug-fix month, brand site, template and audit for $11,300.
The best plan skips the small bug-fix month and takes the brand site, the dashboard, the template and the audit: $12,700, using all 135 hours.
That is $1,400 left on the table by the rate rule. The Freelance Project Picker finds that answer on any list of offers, exactly, and shows the fee at which each declined project would earn its place.
How the plan is found
Offers are sorted by deadline. Your capacity by the end of each week is added up.
Dynamic programming tracks the best total fee for every number of hours used, allowing a project only if the hours used by its deadline still fit.
It then scores highest-fee-first, best-rate-first and listed order, and for each declined project computes the fee at which the plan would include it.
Be honest about hours
Hours estimates run optimistic. Add a scope-creep buffer (20% is common) and the plan will usually drop a project that only fit on paper. Hours you cannot bill (admin, sales, existing clients) belong outside the capacity row.
Questions
Should I take the highest-paying project?
Not automatically. Hours are shared across deadlines, so compare what your whole month earns with and without it: a big project can use hours that two smaller ones would have paid more for.
Is the best hourly rate the right way to choose?
Only if you can fill every hour. A high-rate small project can leave hours nothing else fits into before their deadlines, so the plan with the highest total fee is the one to chase.
How do I decide what to counter-offer on a project I would otherwise decline?
Work out the fee at which it would beat what it displaces. Below that number it costs you money to say yes; at or above it, the project earns its place.