I. XYZ Electronics produces specially coded computer chips for laser surgery in $64MB,256MB,$ and $512MB$ sizes. $(1MB$ means that the chip holds $1$ million bytes of information.$)$ To produce a $64$ MB chip requires $8$ hours of labor, a $256$ MB chip takes $13$ hours, and a $512$ MB chip requires $16$ hours. The XYZ$\text{'}$s monthly production capacity is $1,200$ hours. Mr$.$ Smith, the firm's sales manager, estimates that the maximum monthly sales of the $64MB,256MB,$ and $512MB$ chips are $40,50,$ and $60,$ respectively. The company has the following goals $($ranked in order from most important to least important$)$:

a$.$ Fill an order from the best customer for thirty $64$ MB chips and thirty$-$five $256$ MB chips.

b$.$ Provide sufficient chips to at least equal the sales estimates set by Mr$.$ Smith.

c$.$ Avoid underutilization of the production capacity.

Formulate this problem using goal programming.