Fifth Third Bank in Bloomington, Indiana wants to determine the ATM fee that will maximize its profit from ATM operation. The bank management experimented with a number of fees $($in $0\mathrm{.}25$ increments$)$ at selected ATM machines. The marginal cost of an ATM transaction is $$0\mathrm{.}50.$ The table below provides information on ATM fees and the corresponding usage of ATM.

ATM Fee

ATM Usage

$2\mathrm{.}25$

$0$

$2\mathrm{.}00$

$1,000$

$1\mathrm{.}75$

$1,500$

$1\mathrm{.}50$

$2,000$

$1\mathrm{.}25$

$2,500$

$1\mathrm{.}00$

$3,000$

Which ATM fee maximizes the profit for the bank?

a$.$

$$1\mathrm{.}75$

b$.$

$$1\mathrm{.}50$

c$.$

$$1\mathrm{.}25$

d$.$

$$1\mathrm{.}00$

e$.$

$$2\mathrm{.}00$