1. Quadratic Applications
Maximizing Profit!

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

3. EX: Selling dresses It costs you $10 to make each dress
Other dresses follow the general model q = -20s , 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

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

5. 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.

6. -
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.