Question
A trader realizes 25x-x^2 naira from the sale of X bags of rice.find the sum of bags that will give him the maximum profit?
Answers
Damon
if you do not do calculus find vertex of parabola
x^2 - 25 x = -y
x^2 - 25 x + 625/4 = -y + 625/4
(x-25/2)^2 = -1(y-625/4)
vertex at x = 25/2 and y = 625/4
if you do calculus set derivative (slope) to 0
y = 25x - x^2
dy/dx = 25 -2x
when slope = 0
2 x = 25
x = 25/2 again
x^2 - 25 x = -y
x^2 - 25 x + 625/4 = -y + 625/4
(x-25/2)^2 = -1(y-625/4)
vertex at x = 25/2 and y = 625/4
if you do calculus set derivative (slope) to 0
y = 25x - x^2
dy/dx = 25 -2x
when slope = 0
2 x = 25
x = 25/2 again