Benetton has entered into a quantity flexibility contract with a retailer for a seasonal product. If the retailer orders$$O units, Benetton is willing to provide up to another $40$ percent $($$=0\mathrm{.}4)$ if needed and the retailer commits to buying at least $0\mathrm{.}95$O $($$=0\mathrm{.}05).$ Benetton$$s production cost is $$20,$ and it charges the retailer a wholesale price of $$40.$ The retailer sells to customers at $$60$ per unit. Any unsold units can be sold by the retailer at a salvage value of $$20.$ Benetton can salvage only $$10$ per unit for its leftover inventory. The retailer forecasts demand to be normally distributed, with a mean of $6,000$ and a standard deviation of $1,600.$ The retailer set $$How may units is the retailer expected to salvage?

Group of answer choices

$457$

$278$

$307$

$220$

$109$