Question

A firm has determined that its annual profits depend on the number of sales-people it employs and the amount spent on advertising. Specifically the relationship between profits, π (in Millions), salespeople; S (in thousands) and advertising expenditures, A (in millions), is

π=-10+60S+10A-2S^2-A^2

Determine the number of salespeople and the amount of advertising expenditures that would maximize the firms's profits.

Answer 1

To determine the number of salespeople and the amount of advertising expenditures that would maximize the firms's profits we need to to derive MP function, MP = π' = 0.
So:
MP'(S) = 60 - 4S = 0
S = 15 units
MP'(A) = 10 - 2A = 0
A = 5 units.