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

Question

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