The Cost in Dollars to Produce Q Bottles of a Prescription

question 6

Essay

The cost in dollars to produce q bottles of a prescription skin treatment is given by the function $C(q)=0.08 q^{2}+75 q+900$
.The manufacturing process is difficult and costly when large quantities are produced.The marginal cost of producing one additional bottle when q bottles have been produced is the derivative $\frac{d C}{d q}$
.
a)Find the marginal cost function.
b)Compute C(50)and explain what the number means in terms of cost and production.
c)Compute C'(50)and explain what the number means in terms of cost and production.

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Definitions:

Par Preferred Stock

A type of preferred stock that has a specified face value (par value) which determines the dividend calculation and has priority over common stock in dividend payments and upon liquidation.

Par Common Stock

The nominal or face value assigned to a share of common stock, as declared in the corporate charter, which has little bearing on the market value of the share.

Market Value

The present cost at which a service or asset is available for purchase or sale in the market.

Share-based Compensation

A form of remuneration where employees receive shares of the company's stock as part of their compensation package.