Question #54148

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.

Expert's answer

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.

So:

MP'(S) = 60 - 4S = 0

S = 15 units

MP'(A) = 10 - 2A = 0

A = 5 units.

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