QUESTION TWO $[25$ MARKS$]$

A family is considering whether to invest in solar panels. Some information regarding solar systems and energy in general has been gathered in their home and is summarized below.

The average cost for residential energy is $$\frac{0\mathrm{.}124}{k}Wh$

The government subsidizes $70\%$ of whatever is invested by the household

Each square foot of panel produces $19\mathrm{.}13kWh$ every year

The cost of installation per square foot of solar panel is $$93\mathrm{.}91$

$1$

The family house has $350$ square feet of roof space. Answer the following questions for each of these interest rates: $6\%,12\%,$ and $18\%.$ Provide a complete solution including code snippets utilized in the solution.

a$)$ Write Matlab code to solve for the breakeven points when each of the effective interest rates are prevailing.

b$)$ Write Matlab code to draw profiles of the breakeven analysis criteria at each of the interest rates and superimpose the breakeven boundaries. All these profiles and boundaries should be presented on one graph. Provide legends to identify the different profiles.

c$)$ It is expected that the type of solar system to be utilized has a service life of $25$ years. Make a recommendation of whether it is worth investing in this solar system at each of these interest rates and provide a justification for your recommendation.