Chris Corry has a company$-$sponsored retirement plan at a major brokerage firm. He has the following funds available:

Fund

Risk

Type

Return

$1$

High

Stock

$11\mathrm{.}98\%$

$2$

High

Stock

$13\mathrm{.}18\%$

$3$

High

Stock

$9\mathrm{.}40\%$

$4$

High

Stock

$7\mathrm{.}71\%$

$5$

High

Stock

$8\mathrm{.}35\%$

$6$

High

Blend

$16\mathrm{.}38\%$

$7$

Medium

Blend

$4\mathrm{.}10\%$

$8$

Medium

Blend

$12\mathrm{.}52\%$

$9$

Medium

Blend

$8\mathrm{.}62\%$

$10$

Medium

Blend

$11\mathrm{.}14\%$

$11$

Medium

Blend

$8\mathrm{.}78\%$

$3$

$12$

Low

Blend

$9\mathrm{.}44\%$

$13$

Low

Blend

$8\mathrm{.}38\%$

$14$

Low

Bond

$7\mathrm{.}65\%$

$15$

Low

Bond

$6\mathrm{.}90\%$

$16$

Low

Bond

$5\mathrm{.}53\%$

$17$

Low

Bond

$6\mathrm{.}30\%$

His financial advisor has suggested that at most $40\%$ of the portfolio should be composed of high$-$risk funds. At least $25\%$ should be invested in bond funds, and at most $40\%$ can be invested in any single fund. At least six funds should be selected, and if a fund is selected, it should be funded with at least $5\%$ of the total contribution.

Develop and solve an integer optimization model to determine which funds should be selected and what percentage of his total investment should be allocated to each fund.