# Math

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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 -

-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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