Due to staffing issues, the daily output of a fresh sandwich manufacturer based in New York varies over time and is modeled by the function

Note that t ∈ [0, 365] is measured in days from 1 January. The manufacturer knows that the lunch-time market in lower Manhattan has a near insatiable appetite for sandwiches and it is possible to sell any number at a unit price given by

where again t ∈ [0, 365] is measured in days from 1 January.

a. Determine the maximum output of sandwiches and the day on which this happens.

b. Determine the maximum price it is possible to charge and the day on which this is possible.

c. Determine the maximum daily revenue the sandwich manufacturer is able to generate and the day that this occurs. Comment on your answer.

d. If the manufacturer wishes to shut down for 1 day in the year for maintenance, which day should he choose? 

You should assume that the manufacturer works 365 days a year.

Transcribed Image Text:

1000 x 2 + sin 2л :)] t sandwiches 365