Find the maximum profit that a company can make
Asked by admin @ in Math viewed by 270 People
Find the maximum profit that a company can make, if the profit function is given by p(x) = 41 − 72x − 18x ^2
Answered by admin @
Given, P(x) = 41 - 72x - 18x²
differentiate with respect to x ,
dP(x)/dx = 0 - 72 - 36x = -72 - 36x
now, put dP(x)/dx = 0 = -72 - 36x
x = -2
let's check , d²P(x)/dx² at x = -2
d²P(x)/dx² = -36 < 0
hence, P(x) will be maximum at x = -2
so, maximum value of P(x) = P(-2)
= 41 - 72(-2) - 18(-2)²
= 41 + 144 - 72
= 185 - 72
= 113
hence, maximum profit that a company can make is 113 units .
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