Solve the problem by setting up and solving a system of three linear equations in three variables.
A small company makes three different types of bird houses. Each type requires the services of three different departments, as indicated by the following table.
type A type B type C
cutting dep. 0.1hour 0.2h 0.1h
finishing dep. 0.4h 0.4h 0.3h
assembly dep. 0.2h 0.1h 0.3h
The cutting, finishing, and assembly departments have available a maximum of 37.5, 99.5, and 55.5 work hours per week, respectively.

Question

Solve the problem by setting up and solving a system of three linear equations in three variables.
A small company makes three different types of bird houses. Each type requires the services of three different departments, as indicated by the following table.
                    type A        type B     type C
cutting dep.   0.1hour       0.2h         0.1h
finishing dep.  0.4h           0.4h         0.3h
assembly dep. 0.2h           0.1h         0.3h
The cutting, finishing, and assembly departments have available a maximum of 37.5, 99.5, and 55.5 work hours per week, respectively.