Lesson 1: Applications, Part 1

Example 1: Maximum Revenue (w/ Function)

• A tractor company has found that the revenue from sales of their heavy-duty tractors is a function of the unit price () charged. The revenue () is:

1. What unit price () should be charged to maximise revenue?
2. What is the maximum revenue ()?

Solving Example 1

• Whenever you are dealing with a maximum revenue question, ALWAYS put the function into vertex form. (Complete the Square)

• To maximise revenue, they should charge $1900, The maximum revenue would be $1 805 000.

Example 2: Maximum Revenue (w/o Function)

• Calculators are sold to students for $20 each. 300 students are willing to buy them at that price. For every $5 increase in price, there are 30 fewer students willing to buy a calculator.

1. What selling price () will produce the maximum sales?
2. What will the maximum revenue be? ()

Solving Example 2

• Note: Revenue () is equal to Price () multiplied by Quantity ().
• .
  • .
  • • FOIL, then complete the square.

Solving Example 2, cont.

• From this, we see that .
• We can determine that .

Example 3: Simple Area

• At a concert, organisers are roping off a rectangular area for sound equipment. There is 160m of fencing available to create the perimeter.

1. What dimensions will give the maximum area ()?
2. What is the Maximum Area ()?

Solving Example 3

• We know that both Perimeter () is , where is the length, is the width, and Area () is .

Solving Example 3, cont.

• Now, we've combined the two equations, and are attempting to solve for .
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