Posted by **Math** on Thursday, May 26, 2011 at 4:34pm.

A manufacture 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 a least $14,000 on the commodity?

- Math -
**Henry**, Saturday, May 28, 2011 at 8:21pm
-6X^2 + 30X -10 = 14,

-6X^2 + 30X - 24 = 0,

Divide3 both sides by -6:

X^2 - 5X + 4 = 0,

(X-4)(X-1) = 0.

X-4 = 0,

X = 4.

X-1 = 0,

X = 1.

Production Range: 1000 to 4000 Units.

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