A company operates two cafes. The total daily cost of running the two cafes is
TC = 6000 + 180x + 140y
where x is the number of patrons in cafe one and y the number in cafe two. The total daily revenue from the two cafes is
R = 320x + 250y - 0.375x2 - 0. 5y2 - 0.25xy
Determine the level of patronage required to maximise total profit. How much are these profits?
is a quadratic surface and so there should be exactly one critical point, and it is either a maximum or a minimum for . Ramining the form of shows that in this case it is a maximum.
So the critical point is the solution of the simultaneous equations:
There is probably a non-calculus method for this problem which involves completing the square for the profit, but I would have to think a bit about how that would work.
RonL