$(10$ pts$)$ In $2019,$ Stony Brook Hospital admitted $12,775$ patients. In $2020,$ a $30\%$

increase in admissions is expected. The hospital has $380$ beds. Assume the hospital

operates $365$ days a year and assume one patient per bed.

a$.$ If the average patient stays in the hospital for $7$ days, how many beds were

empty, on average, in $2019?$

b$.$ If the average patient stays in the hospital for $7$ days, how many beds were

empty, on average, in $2020?$

$(10$ pts$)$ An investment proposal will have an annual fixed cost of $$50,000,$

variable cost of $$25$ per unit of output, and revenue of $$45$ per unit of output.

a$.$ What is the break$-$even quantity?

b$.$ To achieve an annual profit of $$40,000,$ what should be the volume of output?