Question

Find the maximum profit that a company can make, if the profit function is given by p ( x ) = 41 − 72 x − 18 x 2

Answer 1

The profit function is given as,

p( x )=41−72x−18 x 2

Differentiate the function with respect to x,

p ′ ( x )=−72−36x(1)

Put p ′ ( x )=0,

−72−36x=0 36x=−72 x=− 72 36 =−2

Differentiate equation (1) with respect to x,

p ″ ( x )=−36 <0

This shows that x=−2 is the point of local maxima for the given function.

So, maximum profit will be,

p( −2 )=41−72( −2 )−18 ( −2 ) 2 =41+144−72 =113

Therefore, the company can make the maximum profit of 113 units.