D1.04: Examples 10–11

Example 10

A certain river in Georgia is polluted with coliform bacteria. This has been blamed primarily on the dairy farmers whose farms are in the watershed of the river. This formula is used to model the cost in dollars, y, to remove p% of the bacterial pollution from the river. How much of the pollution can be removed if $1.0 million is available to spend on this? [latex]y=\frac{380,000p}{100-p}[/latex]

Example 11

A certain kind of appliance is sold for $10 each and the manufacturer can sell all she produces at that price. To produce these appliances requires a fixed cost of $14,220 per month (equipment depreciation, salaries, utilities, etc.) and the variable cost per appliance is $2.10.

  1. Write a formula for the cost of producing x appliances.
  2. Write another formula for the revenue produced by selling x appliances.
  3. Graph both formulas for [latex]0\le{x}\le2500[/latex].
  4. For what value of x is the cost equal to the revenue? (That point on the graph is called the “break-even” point.)