Maximizing Profit! Quadratic Applications. Formulas Profit formula is P = Total Revenue –...
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Maximizing Profit! Quadratic Applications. Formulas Profit formula is P = Total Revenue – Production Costs Total Revenue = price quantity sold Production
Formulas Profit formula is P = Total Revenue Production Costs
Total Revenue = price quantity sold Production Costs = cost per
item quantity sold
Slide 3
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 sold10q This gives us P = sq
10q
Slide 4
Dresses, continued P = sq 10q q = -20s + 1200 P = s(-20s +
1200) 10(-20s + 1200) P = -20s 2 + 1200s + 200s 12000 P = -20s 2 +
1400s 12000 The maximum profit occurs at the vertex
Slide 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.
Slide 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 s 2 term, and 1400, the coefficient
in the s term.
