1. NetSell, a the TV remote control supplier for Lumyn Electronics, has a weekly

ID: 2856119 • Letter: 1

Question

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.

a) The marginal cost is given by derivative of C(q)

C'(q) = 3(0.000004)q2-2(0.03)q+100

C'(10,000) = (0.000012)(10,000)2-0.06(10,000)+100

=> C'(10,000) = 1200-600+100 = 1300-600 = 700

b) Marginal revenue is q times p(q)

Hence R(x) = q(-0.005q + 200) = 0.005q2+200q

Marginal profit is given by P(q) = R(q)-C(q)

=> P(q) = -0.005q2 +200q-0.000004q3+0.03q2-100q-75000

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

P(2000) = -32000+100000+200000-75000= 193000

P(7000) = -1372000+1225000+700000-75000 = 478000

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