# (Originais Teachy 2023) - Question Medium of Math

A businessman needs to maximize the profit of his company by choosing the ideal selling price for a product. The monthly revenue (R) generated by the sale of this product is given by the function R(x) = -0.5x² + 50x, where x is the quantity of products sold, in hundreds. To maximize profit, the businessman needs to identify the point where the profit variation is zero, that is, where the profit function (L) reaches its maximum value. Assuming that the production cost of this product is R$30.00 per unit, determine: 1) The profit function (L) as a function of x, considering that the production cost is R$ 30.00 per unit. 2) The ideal selling price (p) for this product, which maximizes profit, knowing that the maximum monthly demand is 200 units. 3) The maximum profit (Lm) that the company can obtain per month, knowing that the ideal selling price is R\$ 80.00 per unit.

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