Question

SANUMARC produces fingerlings for sell. The quantity x (kg) of these fingerlings demanded each week is related to the wholesale unit price p by the equation P = − 0.006x + 180 The weekly total cost incurred by SANUMARC for producing x kgs of fingerlings is C(x) = 0.000002x3 – 0.02x2 + 120x + 60,00 a. Find the marginal cost function C, [5] b. Find the marginal revenue function R’ [5] c. Find the marginal profit function P’ (5) d. Compute P’(2000) and interpret the results.

Answer 1

a

$c=0.000002x^3-0.02x^2+120x+6000$

marginal cost $=c=\frac{dc}{dx}=0000006x^2-0.04x+120$

b

$P=-0.006x+180$

Revenue=R$=px=-0.006x^2+180x\\$

Marginal Revenue=R'$=\frac{dR}{dx}=-0.012x+180$

c.

Marginal profit$=R'-C'$

$P'=-0.012x+180-0.000006x^2+0.04x-120\\=-0.000006x^2+0.028x+60$

d.

$x=2000\\P'=-0.00000(2000)^2+0.028(2000)+60=92$

This implies that additional profit from selling 2000th unit is 92. Profit is not maximized at this point as marginal profit is not zero