A linear programming computer package is needed.

Greenville Cabinets received a contract to produce cabinets for a major furniture distributor. The contract calls for the

production of $3,300$ small cabinets and $4,100$ large over the next two months, with the following delivery schedule

Greenville estimates that the production time for each small cabinet is $0\mathrm{.}7$ hours and the production time for each large

cabinet is $1$ hour. The raw material costs are $$10$ for each small cabinet and $$12$ for each large cabinet. Labor costs are $$22$

per hour using regular production time and $$33$ using overtime. Greenville has up to $2,400$ hours of regular production time

available each month and up to $1,000$ 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 SaR$=$ regular small cabinets for month $1,SbR=$

regular small cabinets for month $2,$LaR$=$ regular large cabinets for month $1,LbR=$ regular large cabinets for month $2,$

SaO$=$ overtime small cabinets for month $1,$SbO$=$ overtime small cabinets for month $2,$LaO$=$ overtime large cabinets for

month $1,$ and LbO$=$ overtime large cabinets for month $2)$

$)$

Total Production Cost $=$$