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) = 0.4q^3 - 0.03q^2 + 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.  

b.

c.

Step-by-step explanation:

a) The marginal cost function is given by the derivative of the total cost function, in this way the marginal cost function for this company is:

b) The income function is given by the relation .

The marginal revenue function for the company is given by the derivative of the revenue function, in this way the marginal revenue function is:

(c) The profit function of the company is given by the relation , and the marginal utility function is given by the derivative of the utility function, in this way , the marginal utility function is:

When q = 2000, the marginal utility is:

When q = 7000, the marginal utility is:

the answer is d. 75%