QUESTION TWO $[25$ MARKS$]$

A mini$-$hydropower station always utilizes two types of turbines, A and B for power generation because of the hydrologic nature of the power generation site. A mini hydro generation station was constructed in $1980$ in Salah, Oman using turbines A and B that each have a generation capacity of $40$ Mega Watts $[$MW$],$ and $80$ Mega Watts $[$MW$].$ At the time, there weren't good records kept for the manufacture cost of these types of turbines by the supplier because they were rarely required and these were one of a kind produced to meet that specific order. The company that makes these turbines has separate production lines for each type of turbine but of lower generation capacity and keeps good records of their production costs at its manufacturing plant. Supplier company $1980$ records for turbine type A show that it required $$8\mathrm{.}4$ million to produce the $3^{rd}$ turbine, and $$7\mathrm{.}8$ million to produce the $5^{th}$ turbine. $1980$ records also indicate

that for type B turbine, $$17\mathrm{.}2$ million was used to produce the $8^{th}$ turbine while $$15\mathrm{.}7$ million was required to produce the ${20}^{th}$ turbine.

This cost information provided is for a popular size for type A turbine that has a generation capacity of $8$ MW while the popular version of type B turbine has a generation capacity of $16$ MW$.$ Sales records since $1980$ until to date show that there are approximately four times more type A turbines sold than type B turbines.

It has been determined that the composite index for both types of turbines in $1980$ was $450.$ The following Table summarizes the average cost of type A and type B turbines in $1980$ and to date.

$\backslash$table$[[$Year$,$Type A Turbine Average Price $[$Million $$],$Type B Turbine Average Price $[$Million $$]],[1980,8\mathrm{.}0,15\mathrm{.}0],[2024,13\mathrm{.}5,23\mathrm{.}5]]$

A new hydropower project is proposed to be built this year in Salah that will require a $120$ MW type A turbine and $250$ MW type B turbine. Utilize your knowledge of cost estimation techniques to determine how much should be budgeted for each type of turbine in this project.