Math Problem Statement

A florist determines her monthly profit in dollars from selling bridal bouquets using the function p(x) = 15x^2 - 10.5x. What will her monthly profit be if she sells 12 bouquets?

Solution

The given function for the florist's monthly profit is:

p(x)=15x210.5xp(x) = 15x^2 - 10.5x

where xx represents the number of bridal bouquets sold.

We need to calculate the monthly profit when the florist sells 12 bouquets, i.e., substitute x=12x = 12 into the function.

p(12)=15(12)210.5(12)p(12) = 15(12)^2 - 10.5(12)

First, calculate 122=14412^2 = 144, then substitute:

p(12)=15(144)10.5(12)p(12) = 15(144) - 10.5(12) p(12)=2160126p(12) = 2160 - 126 p(12)=2034p(12) = 2034

So, the florist's monthly profit from selling 12 bouquets is $2034.

Would you like further details on the steps?

Here are 5 follow-up questions:

  1. How does the profit function change if the cost per bouquet increases?
  2. What is the minimum number of bouquets the florist must sell to break even?
  3. Can this quadratic function have a maximum or minimum point? If so, where?
  4. What would the profit be if she sells 20 bouquets?
  5. How can you graph this quadratic function to visualize the profit for different sales?

Tip: For quadratic functions like this, if the coefficient of x2x^2 is positive, the parabola opens upwards, indicating a minimum point.

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Math Problem Analysis

Mathematical Concepts

Algebra
Quadratic Functions
Profit Calculation

Formulas

p(x) = 15x^2 - 10.5x

Theorems

Substitution of a specific value into a function

Suitable Grade Level

Grades 9-10