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 $2)$

$(SaR,SbR,$LaR,$LbR,$SaO,SbO,LaO,LbO$)=($

Total Production Cost $=$$$)$