```ts
export function cutRoll(length: number, board: [number, number][]): Cut {
  if (length < 0 || !Number.isInteger(length)) {
    throw new Error("Length must be a non-negative whole number");
  }

  const dp = Array.from({ length: length + 1 }, () => ({ takings: 0, pieces: [] as number[] }));

  for (let i = 1; i <= length; i++) {
    for (const [metres, price] of board) {
      if (i >= metres && dp[i - metres].takings + price > dp[i].takings) {
        dp[i] = { takings: dp[i - metres].takings + price, pieces: [...dp[i - metres].pieces, metres] };
      }
    }
  }

  return dp[length];
}

type Cut = { takings: number; pieces: number[] };
```