Dividing Partnership Income

is to devote full time. The following plans for the division of income are being considered:

a$.$ Equal division.

b$.$ In the ratio of original investments.

c$.$ In the ratio of time devoted to the business.

d$.$ Interest of $6\%$ on original investments and the remainder equally.

e$.$ Interest of $6\%$ on original investments, salary allowances of $$50,000$ to Black and $$70,000$ to Shannon, and the remainder equally.

f$.$ Plan $($e$),$ except that Shannon is also to be allowed a bonus equal to $20\%$ of the amount by which net income exceeds the total salary allowances.

Required:

$(1)$