A company is evaluating a lockbox system proposal. The average number of payments received by the company per day is $1,500$ and the average payment amount is $$200.$ The bank proposing th system will charge the company a variable cost of $$0\mathrm{.}05$ per transaction $($i$.$e$.$ payment proceeds$)$ in addition to a $$5000$ annual fee. The bank has eliminated that use of the lockbox system will reduce the companies collection time by two days. The annual interest rate is $6\%$ a$)$ should the proposed lockbox system be accepted? b$)$what is the maximum annual fee the company should pay for this lockbox system?