Previous Problem Problem List Next Problem (8 points) ADTF Distributors has found that the relationship between the price p (in dollars) and the demand a for a particular gadget given approximately by p = 1572.04 - 0.17x2. The company also knows that the cost (in dollars) of producing the product is given by C(x) = 820 + 397x. (a) Find P(a), the profit function. P(a) = (b) List all the critical values of P(x). The critical values are x = (list all values, separated by commas) Hint: One of the critical values found in part (b) will be negative. Although this negative value is included as an answer in part (b), it must then be excluded below, since a is not allowed to be negative in this context. (c) Use the answers and functions above to complete the following sentence. Round to the nearest cent. In order to maximize their profit, ADTF Distributors should produce and sell gadgets. The selling price will b and the maximum total profit will be $