Lindsay has worked for a landscaping company for the past two summers. Next year, she plans to start her own lawn care business. She has nine clients lined up and has scheduled half a day per week for each client, leaving a half day each week for maintenance and the day to day running of the business. She plans to work for $6$ months each year, from mid$-$April to mid$-$October, and wants to keep her business going for the next four years.

Lindsay plans to borrow, as necessary, to get her business started. She earned about $$6000$ every summer at her previous landscaping job, but she wants to make more than that with her own business.

Lindsay will have the following costs to run her landscape business.

$$ She has three options for getting a lawn tractor and trailer:

a$)$ Buy used with $$7600$ bank loan at $8\mathrm{.}3\%,$ compounded monthly, with payments of $$175$ per month. The loan must be paid monthly, regardless of if she is working or not. She is responsible for the maintenance of the equipment

b$)$ Lease for $$600$ down and $$1775$ for $6$ months. This will be repeated for each of the $4$ years.

c$)$ Rent for $$100$ per week $($assume $26$ weeks$)$

$$ Tools will cost $$1700.$ She plans to buy them with a credit card A at $19\mathrm{.}5\%,$ compounded daily.

$$ Miscellaneous materials and work clothes will cost $$1100.$ She plans to use credit card B at $16\mathrm{.}5\%,$ compounded daily.

$$ Gas for her work truck and her tractor will cost $$200$ per month for the months she works, which she will pay cash.

$$ Every year she will have other operating costs of $$550,$ which she will pay cash.

Answer the following questions showing all your workings, $$How much should Lindsay charge each client per season?$.$

a$)$ Compare Lindsay$$s options for getting a lawn tractor and a trailer. Which option would you recommend? Explain.

b$)$ Lindsay will make $$100$ monthly payments on each credit card from mid$-$April to mid$-$October. What will be the balance on each credit card after $6$ months? How much interest will she pay altogether?

c$)$ At the end of her first work season, Lindsay consolidated her credit card debt in a line of credit at $6\mathrm{.}2\%,$ compounded monthly, and then paid it off in $6$ monthly payments. How much interest did she pay to consolidate her debt?

d$)$ For this question only, assume Lindsay chose to purchase the tractor and trailer, regardless of your choice. After four seasons, Lindsay will sell her tractor and trailer $($depreciated at $15\%$ per year$)$ and tools $($depreciated at $30\%$ per year$).$ How much equity will she have after $4$ years?

e$)$ What will her total costs be $($this includes tractor, tools, clothes and all other operating expenses$),$ per season, if they are averaged out over $4$ seasons?

f$)$ Based on her costs and expected income, how much should she charge each client, per $6$ month season, that is reasonable yet will exceed her previous job$$s income? Explain.