Please answer all parts of the following question (you must use Caclulus concept

ID: 2869390 • Letter: P

Question

Please answer all parts of the following question (you must use Caclulus concepts learned and show all work):

1. NetSell, a TV remote control supplier for Lumyn Electronics, has a weekly production cost of q TV remote controls that is given by

C(q) = 0.000004q3 - 0.03q2 + 100q + 75,000

where q is in the interval [0, 10,000].

The demand function for this product is given by

p(q) = -0.005q + 200.

Based on this information, find the following:

a) The marginal cost for the company.

b) The marginal revenue for the company.

c) The marginal profit for the company when 2,000 and 7,000 TV remote controls are manufactured.

(a) the marginal cost for the company= c'(q)= 0.000004*3q^2-0.03*2*q+100=0.000012q^2-0.06q+100

b) The marginal revenue for the company= R'(q)

since R(q)=q*p(q)=q*(-0.005q+200)=-0.005q^2+200q

R'(q)=-0.005*2q+200=-0.01q+200

(c) profit function P(x)= R(q)-C(q)=(-0.005q^2+200q)-(0.000004q^3 - 0.03q^2 + 100q + 75,000)

=-0.000004q^3 +0.025q^2 + 100q - 75,000

so, The marginal profit=P'(q)=-0.000004*3q^2+0.025*2q+100

= -0.000012q^2+0.05q+100

when q= 2000, The marginal profit=P'(2000)= -0.000012(2000)^2+0.05(2000)+100=152

when q= 7000, The marginal profit=P'(7000)= -0.000012(7000)^2+0.05(000)+100= -138?

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