Find the fewest paid minutes needed to reach a gross earnings goal across several fixed-rate opportunities. Enter each opportunity’s required minimum and available maximum time.

Use up to two decimal places. Gross amounts exclude taxes and deductions.

Every listed minimum is mandatory, even when another job alone could meet the goal. Use 0 when a job has no minimum.

Enter fixed USD/hour rates (0–1,000,000; up to 2 decimals) and whole paid-minute bounds (0–1,000,000 per bound). Maximum must be at least minimum.

Job 1

Job 2

Finds one allocation with the fewest paid minutes, using every minimum and the entered caps. It does not minimize extra earnings or check clock-time conflicts, overtime or take-home pay.

After Calculate, active inputs are saved in this browser. Other scripts on this site may access saved values. Reset clears this calculator’s saved data.

Work Hours Allocation Formula

The calculator chooses whole-minute allocations mᵢ to minimize total paid time while meeting the entered gross goal:

Minimize Σmᵢ
Subject to Σ(rᵢ × mᵢ ÷ 60) ≥ G
And lᵢ ≤ mᵢ ≤ uᵢ for every opportunity

Here, rᵢ is the fixed USD hourly rate, lᵢ is the mandatory minimum time, uᵢ is the available maximum time, and G is the gross USD goal. All time bounds and allocations are whole minutes. Earnings are compared before display rounding; row amounts show four decimal places, with a cent-rounded grand total.

How the Allocation Works

Every listed minimum is assigned first. Those commitments contribute both time and earnings, even when they already exceed the goal. Maximum reachable earnings equal Σ(rᵢ × uᵢ ÷ 60); a larger goal produces a shortfall instead of a feasible allocation.

If more earnings are needed, the remaining minutes go to the highest-rate opportunity with unused capacity, then the next highest. The final required portion rounds upward to a whole minute, so the result can exceed the goal.

This minimizes paid minutes because every additional minute has the same duration. Replacing a lower-paid extra minute with an available higher-paid minute preserves time and cannot reduce earnings. The highest-paying available minute sequence therefore reaches the goal with the fewest additional minutes under these bounds.

The model uses constant supplied rates within one planning period. It does not place hours on a calendar, resolve overlapping availability, change rates for overtime, or calculate taxes. Minimums apply to every listed opportunity; an optional commitment should not be entered as mandatory.

How to Use the Calculator

  1. Select 2 to 5 opportunities and enter their fixed USD hourly rates.
  2. Enter each required minimum and available maximum as whole minutes. Keep every maximum at least as large as its minimum.
  3. Enter the gross earnings goal for the same planning period.
  4. Select Calculate. Review the allocation, total paid time, earnings, and capacity or shortfall.

Worked Example

For a USD 500 goal, enter these opportunities:

  • A: USD 40/hour, minimum 120 minutes, maximum 300 minutes.
  • B: USD 25/hour, minimum 0 minutes, maximum 1,200 minutes.
  • C: USD 20/hour, minimum 0 minutes, maximum 600 minutes.

A’s required two hours produce USD 80. Filling A to its five-hour cap produces USD 200. The remaining USD 300 takes 12 hours at B’s rate.

The allocation is A = 300 minutes, B = 720 minutes, and C = 0 minutes: 1,020 minutes, or 17 paid hours. Gross earnings are 5 × 40 + 12 × 25 = USD 500. The stated maximums could produce USD 900 in total.

Frequently Asked Questions

What happens if the goal is zero?

All mandatory minimums still apply. Set a minimum to zero when no time is required for that opportunity.

Can several allocations use the same minimum time?

Yes. Equal rates or the final whole minute can allow alternatives. The calculator returns one allocation using its rate ordering; it does not minimize excess earnings as a second objective.

Why might row amounts add to a slightly different total?

Displayed row amounts are rounded to four decimals. The total uses the unrounded earnings before rounding to cents.

Sources