Question

Y=X+4X²-0.2X³ (Y=is wheat fields in kgs and X=amount of ferterlizer applied) Derive MPP and APP of the variable factor

Answer 1

MPP $= \frac{dY}{dx} = 1 + 8x - 0.6x^{2}$

APP $= \frac{Y}{x} = 1 + 4x -0.2x^{2}$

MPP is maximum when $\frac{\delta MPP}{\delta x} = 0$

$8-1.2x = 0$

$1.2x = 8$

$x = 6.67$

APP is maximum when $\frac{\delta APP}{\delta x} = 0$

$4-0.4x = 0$

$0.4x = 4$

$x = 10$