$A$ factory makes tennis rackets and cricket bats. $A$ tennis racket takes $1.5\, \text{hours}$ of machine time and $3\, \text{hours}$ of craftsman's time in its making, while a cricket bat takes $3\, \text{hours}$ of machine time and $1\, \text{hour}$ of craftsman's time. In a day, the factory has the availability of not more than $42\, \text{hours}$ of machine time and $24\, \text{hours}$ of craftsman's time. What number of rackets and bats must be made if the factory is to work at full capacity?

• A
  $x=4, y=12$
• B
  $x=6, y=10$
• C
  $x=8, y=6$
• D
  $x=10, y=4$