Question
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?
-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?
Answers
-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.
-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.