GAP Co$.$ Inc. is producing a product which requires three parts at the final assembly stage. These three parts can be produced by two different departments as detailed below.

Production rate $($units$/$hr$)$

Part $1$ Part $2$ Part $3$ Unassembled parts Cost $($$$/$hr$)$

Department $187102530\mathrm{.}0$

Department $271262517\mathrm{.}5$

In a week, $1,100$ finished $($assembled$)$ products are needed $($but up to $1,350$ can be produced if necessary$).$ If department $1$ has $100$ working hours available, but department $2$ has $110$ working hours available, the company needs to formulate a model that will minimize the cost of producing the finished $($assembled$)$ products needed this week as an LP$,$ subject to the constraint that limited storage space means that a total of only $200$ unassembled parts $($of all types$)$ can be stored at the end of the week.

Note: because of the way production is organized in the two departments it is not possible to produce, for example, only one or two parts in each department, e$.$g$.$ one hour of working in department $1$ produces $8$ part $1$ units, $7$ part $2$ units and $10$ part $3$ units and this cannot be altered.

Provide the needed Decision Variables. List all possible variables.