A linear programming computer package is needed.

Greenville Cabinets received a contract to produce speaker cabinets for a major speaker manufacturer. The contract calls for the production of $3,300$ bookshelf speakers and $4,100$ floor speakers over the next two months, with the following delivery schedule.

Model Month $1$ Month $2$

Bookshelf $2,1001,200$

Floor $1,5002,600$

Greenville estimates that the production time for each bookshelf model is $0\mathrm{.}7$ hours and the production time for each floor model is $1$ hour. The raw material costs are $$10$ for each bookshelf model and $$12$ for each floor model. Labor costs are $$22$ per hour using regular production time and $$33$ using overtime. Greenville has up to $2400$ hours of regular production time available each month and up to $1000$ additional hours of overtime available each month. If production for either cabinet exceeds demand in month $1,$ the cabinets can be stored at a cost of $$5$ per cabinet. For each product, determine the number of units that should be manufactured each month on regular time and on overtime to minimize total production and storage costs. Round your answers to the nearest integer. $($Let BaR $=$ regular bookshelf units for month $1,$ BbR $=$ regular bookshelf units for month $2,$ FaR $=$ regular floor units for month $1,$ FbR $=$ regular floor units for month $2,$ BaO $=$ overtime bookshelf units for month $1,$ BbO $=$ overtime bookshelf units for month $2,$ FaO $=$ overtime floor units for month $1,$ and FbO $=$ overtime floor units for month $2)$

$($BaR$,$ BbR$,$ FaR, FbR$,$ BaO, BbO, FaO, FbO$)=$

Total Production Cost $=$ $