Same problem as Problem $1,$ except that we now add a fifth goal:

$$ G$5$: Achieve steel usage of as close to $9,000$ lbs as possible

The Company plans on switching to a different type of steel for the next production period, so they have to use up as much of the available steel inventory as possible.

Furthermore, the manager, in consultation with his advisors, decided to rank the five goals based on company priorities:

$$ Rank $1$: G$1$

$$ Rank $2$: G$5($penalty $=1$ per each $$1$ deviation$)$

$$ Rank $3$: G$2,$ G$3,$ G$4($assume penalty for each rank $3$ goal remains $1)$