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The following is a simple, but classical model of business planning. We assume that the quantity of product that a business will sell depends on the sale price set by the business, according to a function s(p). Note that the model requires p ≥ 0, and s(p) ≥ 0. Each item sold will obviously bring in a revenue of p. This allows us to determine total revenue as a function of the price, R(p). Production and sales, however, also entail a cost. We may assume that there is a fixed cost c, regardless of how many items are sold, and a variable cost, which depends on the number of items sold, v(s): Tota

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