Please answer all parts of the following question (you must show all work): 1. N

ID: 2867117 • Letter: P

Question

Please answer all parts of the following question (you must show all work):

1. NetSell, a the 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.

we need revenue and profits functions and marginal functions

Revenue R(q) = q (-0.005q + 200) = 200q - 0.005q2

Profit P(q)= revenue - production cost = 200q - 0.005q2 - (0.000004q3 - 0.03q2 + 100q + 75,000)

P(q) = -75000 +100q +0.025q2 - 0.000004q3

marginal cost function C '(q) = 100 - 0.06q + 0.000012q2

marginal revenue func R '(q) = 200 - 0.01q

marginal profit function P '(q) = 100 + 0.05q - 0.000012q2

so when 2000 remote controls are manufactured (put q = 2000)

a.)marginal cost C '(q) =100 - 0.06 (2000) + 0.000012 (2000)2 = 28

b.)marginal revenue R '(q) = 200 - 0.01(2000) = 180

c.)marginal profit P '(q) = 100 + 0.05 (2000) - 0.000012 (2000)2 = 152

so when 7000 remote controls are manufactured (put q = 7000)

a.)marginal cost C '(q) =100 - 0.06 (7000) + 0.000012 (7000)2 = 268

b.)marginal revenue R '(q) = 200 - 0.01(7000) = 130

c.)marginal profit P '(q) = 100 + 0.05 (7000) - 0.000012 (7000)2 = -138

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