$($a$)$ How many of each type of vessel should be used to keep the operating costs $C$ to a minimum?

The minimum is $C=|$

$at(x,y)=(,).$

$($b$)$ Suppose $C=cx+54,000y.$ Find the range of values that the cost of operating a type A vessel, the coefficient $c$ of $x,$ can assume without changing the optimal solution.

$c$

$($c$)$ Find the range of values that Requirement $1$ for deluxe cabins can assume. $($Requirement $1$ pertains to the deluxe cabin requirement.$)$