A convenience store sells spicy black bean burritos during the weekday lunch hour. It charges $

$6\mathrm{.}00$

$$for each burrito and the burritos are purchased from a local manufacturer for $

$1\mathrm{.}75$

$$each$.$ Any burritos left at the end of the day are disposed of and have no salvage value. The manufacturer's production cost is $

$1\mathrm{.}00$

$$per burrito. Burrito demand follows a normal distribution with a mean of

$200$

$$and a standard deviation of

$40$

What is the minimum buy back price the manufacturer could offer the convenience store in order to get them to order $170?$