You have a new job as a Financial Planning assistant. Your client wants to invest money in stocks, bonds, and treasuries that have the dividend yields shown in the table below. Your job is to allocate their money across these three investments such that the total dollars of stocks is at least $$10,000$ less than the total dollars in bonds plus treasuries. In addition, they have identified the maximum investment in each of those three investment types $($also shown below$).$ Maximize the dividends earned.

Your answer will be the amount invested in Stocks $($rounded to whole dollars$).$

Use Scenario $4$

Scenario $1$ Scenario $2$ Scenario $3$ Scenario $4$

Stocks: yield $\%2\mathrm{.}221\mathrm{.}711\mathrm{.}141\mathrm{.}25$

Bonds: yield $\%2\mathrm{.}041\mathrm{.}983\mathrm{.}031\mathrm{.}48$

Treasuries: yield $\%1\mathrm{.}931\mathrm{.}882\mathrm{.}082\mathrm{.}55$

Stocks: $ max $170,000400,000410,000800,000$

Bonds: $ max $60,000180,000300,000280,000$

Treasuries: $ max $50,000200,00075,000500,000$