Q$.4($a$)$ A youth hostel has an electrical demand of $80kW$ and hot

water demand of $180kW.$ The average annual load factor

is $0\mathrm{.}8.$ At present, it is using a gas boiler to provide daily hot

water and purchasing electricity to run the hostel's

appliances. The owners of the youth hostel are considering

installing a solar power system that will use gas with a heat$-$

to$-$electricity ratio of $1\mathrm{.}7$:$1$ to generate electricity. If the heat

output of the solar system is insufficient, the existing gas

boiler will supplement the heat output. The initial cost of the

solar power system installation is $$160,000.$

Given:

Efficiency of the gas boiler $=75\%$

Electric power output of solar system $=80kW$

Gas power input of solar system $=260kW$

Unit price of electricity is $$\frac{1\mathrm{.}2}{k}Wh$

Unit price of gas is $$\frac{0\mathrm{.}9}{k}Wh$

Existing gas boiler maintenance cost is $$12,\frac{000}{?}$ year

Solar system maintenance cost is $$8,\frac{000}{?}$ year

$($i$)$ Determine the simple payback period if the solar

system unit is used.