$($b$)$ Renewable energy is the future source of energy in our daily lives. Many

investment companies have started to invest in various renewable energy

technologies. Suppose a company has RM $1$ million, and there are three

renewable energy investment options: solar energy, wind energy, and

geothermal energy. If there is no investment made to the corresponding

renewable energy, the return on investment will be zero. The investment is done

in multiples of RM $200$k$.$ If $d_i($in million$)$ is invested in investment $i,$ the return

on investment, $r_i$ for each renewable energy is as follows for:

Solar Energy, $i_1$

$r_1(d_1)=0\mathrm{.}2d_1+0\mathrm{.}6$ for $d_1>0,if{d}_{1}0,$ then $r_1(d_1)=0$

Wind Energy, $i_2$

$r_2(d_2)=0\mathrm{.}3d_2+0\mathrm{.}4$ for $d_2>0,if{d}_{2}0,$ then $r_2(d_2)=0$

u$.2d_1$

Geothermal Energy, $i_3$

Geothermal Energy, $i_3$

$r_3(d_3)=0\mathrm{.}4d_3+0\mathrm{.}3$ for $d_3>0,if{d}_{3}0,$ then $r_3(d_3)=0,-\frac{0\mathrm{.}6}{0\mathrm{.}2}$

$($i$)$ Determine the investment to be made to maximize the return on

investment.

$(10$ marks$)$

$($ii$)$ Calculate the maximum amount of return on investment.

$[$Total: $25$ marks$]$help