# Meeting Profit Goals

• May 13th 2009, 07:28 AM
clari
Meeting Profit Goals
A manufacturer of a certain commodity has estimated that her profit in thousands of dollars is given by the expression
-6x^2 + 30x -10

where x (in thousands) is the number of units produced. What production range will enable the manufacturer to realize a profit of at least \$14,000 on the commodity?
• May 14th 2009, 04:23 AM
The Second Solution
Quote:

Originally Posted by clari
A manufacturer of a certain commodity has estimated that her profit in thousands of dollars is given by the expression
-6x^2 + 30x -10

where x (in thousands) is the number of units produced. What production range will enable the manufacturer to realize a profit of at least \$14,000 on the commodity?

Solve $-6x^2 + 30x - 10 > 14 \Rightarrow -6x^2 + 30x - 24 > 0 \Rightarrow x^2 - 5x + 4 < 0$.