## Related questions with answers

Cassie and Cliff decided that their company would specialize in designing Web logs, or "blogs." Since production of any blog requires about the same amount of programming time, each customer could be charged the same price. Cassie and Cliff also estimated that the number of customers in a year would be related to the price. by n(x) = 600 - 2x, where x is the price charged per blog. Production of each blog will require about $200 in programmer labor. To get started in business, they bought a computer for$2,000. (a.) Write rules for the following functions, simplifying where possible. i. Annual income from blog designs I(x) if the price is x dollars per blog. ii. Annual production costs for blog designs C(x) if the price is x dollars per blog. iii. Annual profit from the business P(x) if the price is x dollars per biog. iv. Profit per customer $P_{c}(x)$ if the price is x dollars per blog. (b.) What would be reasonable domains for the functions in Part a? (c.) For what blog prices would the following functions be maximized? i. Income I(x). ii. Profit P(x). iii. Profit per customer $P_{\mathrm{c}}(x)$ (d.) What price would you recommend that Cassie and Cliff charge per blog? Explain your reasoning.

Solution

Verifieda. i. The income is given by the product of the number of customers and the price. This can be written as follows:

$\begin{aligned} I(x)&=x(600-2x)\\ &=600x-2x^2 \end{aligned}$

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