Quadratic Applications Maximizing Profit!

Formulas Profit formula is P = Total Revenue – Production Costs Total Revenue = price • quantity sold Production Costs = cost per item • quantity sold

EX: Selling dresses It costs you $10 to make each dress Other dresses follow the general model q = -20s + 1200, where q is the quantity (number sold) and s is the selling price P = Total Revenue – Production Costs, so: Revenue = price • quantity sold… sq Production Costs = cost per item • quantity sold…10q This gives us P = sq – 10q

Dresses, continued P = sq – 10q q = -20s + 1200 P = s(-20s + 1200) – 10(-20s + 1200) P = -20s2 + 1200s + 200s – 12000 P = -20s2 + 1400s – 12000 The maximum profit occurs at the vertex…

By finding the vertex of the parabola, we will find the selling price that will generate the most profit. The x-axis represents selling price, so the value of the x-coordinate at the vertex represents the best price. The y-value at the vertex will give the amount of profit made.

- The selling price that generates the maximum profit is $35 Find the x-coordinate of the vertex by applying the formula . In this case, the variable is s rather than x. The other values are a = - 20, the coefficient in the s2 term, and 1400, the coefficient in the s term.