The Rio Credit Union has $$250,000$ available to invest in a $12-$month commitment and wants to invest all of it$.$ The money can be placed in Brazilian treasury notes yielding an $8\%$ return or in riskier high$-$yield bonds at an average rate of return of $9\%.$ Credit union regulations require diversification to the extent that at least $40\%$ of the investment be placed in Treasury notes. It is also decided that no more than $30\%$ of the investment be placed in bonds.

The aim of the objective function for Rio Credit Union should be to Maximize the objective value.

Decision variables:

$x=$$ invested $in$ Treasury notes

$Y=$$ invested $in$ Bonds

Objective function $($in decimals, eg$.,\mathrm{.}07,$ NOT $7\%)$:

$Z=$ROI$=\mathrm{.}08x+Y$

Subject to:

$1x+1Y,=$$$250,000(C_1)$

$1x+0Y,$$$100,000(C_2)$

$0x+1Y,$$$75,000(C_3)$

$x,Y0,$

On the graph on right, constraints $C_1,C_2$ and $C_3$ have been plotted using the line plotting tool.

Using the point drawing tool, plot all the corner points for the feasible area.

In this case, the feasible area lies the line plotted for constraint $C_1$

The optimal ROI occurs when:

$x=175,000(enter$ your response $as$ a whole number$).$

$Y=(enter$ your response $as$ a whole number$).$