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What is the equation for this problem?

A company (Widgets, Inc.) is a linear function of price information-based Widget Next: What is the x number of players sold, and p (x) the price for dollars widget. The company started selling x = 300 players at a price flat $ 70 each. After holding a "sale", the company offers a $ 10 discount on the price increase more than 20 players sold. (A) Find a linear function of prices p (x) on the basis of such information. (B) Based on the fact that the company wants both sales and prices is positive, what is the proper domain of the function of prices p (x)? Domain (c) What is the function of income? (Revenue is the total sales revenue) (d) What is the selling price p yields the maximum revenue?

(A) P (x) = a + b = bx delta (p) / delta (x) delta (x) = 20, Delta (p) 10 b =- =- 70 = 1.2 So 1 / 2 *- 300 150 = 220 = 70 so I finally know p (x) = x 220-1/2 * (b) the area of the pricing function is of 0 <= <X = 440 (c) R (x) = p (x) = x * 220 * x-1 / 2 * x ^ 2 (d) Calculate x for which R (x) is maximum, then , set p ( x) for values of p. To calculate the optimal maximum amount is not necessary derivatives. You can see that the graph of R (x) is a parabula, which has a maximum halfway between x = 0 and x = 440 (The ends of the field in which p and R are positive). Therefore x_max = 440 / 2 = 220, p (x) = 220-1/2 * 220 = $ 110

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