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In Business Mathematics and Statistics, the corresponding price and maximum profit can be determined by using the relationship between the demand function, price, revenue, cost, and profit. However, the numerical information required to calculate a specific price and maximum profit is not included in the question provided. Therefore, the general mathematical procedure used for finding the corresponding price and maximum profit is explained below. Suppose the demand or quantity function is given by [ q=f(p) ] where (q) represents the quantity demanded and (p) represents the price per unit. The total revenue earned by the firm is obtained by multiplying price by quantity sold. Thus, [ R=pq ] or, after substituting the demand function, [ R(p)=p f(p). ] Suppose the total cost of producing and selling (q) units is represented by the cost function [ C=C(q). ] The profit function is obtained by subtracting total cost from total revenue: [ P=R-C. ] Hence, [ P(p)=R(p)-C(q). ] The objective is to find the value of price (p) at which profit __________ ________ _________ ______ ____ __________ _________ _________ ______ ___.
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