Precalculus word problem

Question

A cupcake bakery has determined that their weekly profit in thousands of dollars is given by -2x^2+12x-6, where x is the number of cupcakes baked and sold, in hundreds. What is the range of cupcakes they must bake and sell in a week in order to have a weekly profit of at least $10,000?

Answer 1

-2x^2+12x-6 >= 10 [ since the equation of price is in thousands]

Solving for the above inequality:

Dividing both sides by 2:

-x^2+6x-3>=5

or, -x^2+6x-8>=0

or, (2-x)(x-4)>=0

the above condition is only possible for values of x, given by 2>= x >= 4

in the above range for the factors of the inequality is -ve or zero making the product zero or +ve.

Thus the range of cupcakes to be baked is greater than or equal to 200 but less than or equal to 400.

:) Hope this helps.