Maths algebric sums included C(x)

Question

Suppose C(x)=4x2-28x+73,x>=0, represent the cost ,in hundreds of dollars to produce x thousands of pens find the number of pens which can be produced for no more than $2500.

Between ____ thousand and. ___ thousands pens

Answer 1

C(x) = 4x^2 -28x + 73 < 2500

4x^2 - 28x < 2528

x^2 - 7x < 632

x^2 -7x +49/4 < 632 - 49/4 = 621.75

(x-7/2) < sqr621.75 = 24.935

x < 27.435

x is between 27,000 pens and 28,000 pens