GreenTech Solar Solutions, Inc. which has a $1-$year contract to produce $100,000$ solar panels for a new sustainable housing project. The owner, Dr$.$ Elena Green, is optimistic that the contract will be renewed with an increased order volume next year. Dr$.$ Green has evaluated costs associated with three manufacturing technologies: Traditional Assembly Line $($TAL$),$ Modular Construction System $($MCS$),$ and High$-$Efficiency Automated Assembly $($HEAA$).$ The cost data for these options are as follows:

$$

$$Traditioanl Assembly Line$($TAL$)$

Modular Construction System$($MCS$)$

High Efficiency Automated Assembly Line$($HEAA$)$

Annual contracted units

$100,000$

$100,000$

$100,000$

Annual fixed cost

$$80,000$

$$160,000$

$$400,000$

Per unit variable cost

$$20\mathrm{.}00$

$$18\mathrm{.}00$

$$15\mathrm{.}00$

a$.(6$ points$)$ Solve for the crossover points. Show all work

b$.(3$ points$)$ The option TAL is best when the contracted volume is between $\_\_\_\_\_\_\_\_\_\_\_\_\_\_$and $\_\_\_\_\_\_\_\_\_\_\_\_\_$ units

units $($enter your response as a whole$$ number$).$

The option MCS is best when the contracted volume is between $\_\_\_\_\_\_\_\_\_\_\_\_$ and $\_\_\_\_\_\_\_\_\_\_$ units

$.$

The option HEAA is best when the contracted volume is over $\_\_\_\_\_\_\_\_$ units

c$.(2$ points$)$ What is the cost to make $100,000$ units using the cheapest process.