The AB-XYZ company has hired a M121 commerce student who successfully completed a calculus course to estimate the break-even point for a manufacturer of smoke alarms. By checking the past records of costs and output, the student has determined that the variable cost per smoke alarm is $30 when the output is very low, is $18 when the output is 30 smoke alarms per hour, and drops toward $10 when the output is very high; the fixed cost is 300 per hour; and each smoke alarm made can be sold for $20. 

(a.) Write the AB-XYZ company's variable cost v as a linear-to-linear rational function of output level q, i.e., in the form v=(aq+b)/(q+c). 

(b.) Write the AB-XYZ company's total cost C as a quadratic-to-linear rational function of the output level q. 

(c.) Determine the output level q at which the AB-XYZ company must operate to break-even.