) A firm estimates that it can sell Q units of its product with an advertising expenditure of x thousand dollars where = () = − ଶ + 600 + 25 i) Over what level of advertising expenditure is the number of units of product sold increasing? ii) Over what level of advertising expenditure is the number of units of product sold decreasing?
Answers
Given : A firm estimates that it can sell Q units of its product with an advertising expenditure of x thousand dollars where
Q(x)= -x² + 600x + 25
To Find : i) Over what level of advertising expenditure is the number of units of product sold increasing?
ii) Over what level of advertising expenditure is the number of units of
product sold decreasing?
Solution:
Q(x)= -x² + 600x + 25
dQ/dx = -2x + 600
Over what level of advertising expenditure is the number of units of product sold increasing
=> dQ/dx > 0
=> -2x + 600 > 0
=> x < 300
for Expenditure upto 300 thousand dollars the number of units of product sold increasing
Over what level of advertising expenditure is the number of units of
product sold decreasing
dQ/dx < 0
=> -2x + 600 < 0
=> x > 300
for Expenditure above 300 thousand dollars the number of units of product sold decreasing
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