Formulate integer $($or mixed integer$)$ programming models for the following. $($Do not attempt to solve the problems.$)($a$)\{$The Knapsack Problem$)$ A backpacker's knapsack has a volume of V in$\mathrm{.}3$ and can hold up to W lb of gear. The backpacker has a choice of n items to carry in it$,$ with the i$\backslash$h item requiring a$,$ in$\mathrm{.}3$ of space, weighing w$,-$ lb$,$ and providing c$,$ units of value for the trip. What items should be taken in the knapsack? $($b$)$ Refine part $($a$)$ to include the following considerations: Item $1,$ a can of tuna fish, Item $2,$ a can of corn, and Item $3,$ a can of stew, have no value unless Item $4,$ the can opener, is taken; and only one snack, either Item $5,$ potato chips $($light but bulky$),$ or Item $6,$ unpopped popcorn $($small but heavy$),$ is to go$.$ Of course Items $2,3,$ and $6$ all use Item $7,$ the cooking pot.