I have worked this out but apparently I'm setting up the problem wrong

Question

An accounting firm has 780 hours of staff time and 272 hours of reviewing time available each week. The firm charges $1800 for an audit and $200 for a tax return. Each audit requires 60 hours of staff time and 16 hours of review time. Each tax return requires 10 hours of staff time and 4 hours of review time. What numbers of audits and tax returns will yield an optimal revenue?

 

audits $

 

tax returns $

What is the optimal revenue?

Answer 1

variables/knowns

a=audit

t=return

s=staff time

s=60a+10r

r=review time

r=16a+4r

o=optimized revenue

 

780>=60a+10r

-10r>=60a-780

r>=-6a+78

 

272>=16a+4r

-4r>=16a-272

r>=-4a+68

 

the final piece of the puzzle is determining the optimum revenue.

 

1800a+200b=o

1800a-o=-200b

-9a+o/200=b

 

since this is an equation of the total revenue the -slope (-9a) tells us that the revenue will always be higher if we increase the amount of audits.  The maximum amount of audits that can be done is 13.

 

 

The amount of the optimal revenue is  $23,400.