A building contractor has just won a contract to build a municipal library building. His present labor work force is inadequate to take this work immediately as he has already got other jobs on hand.

Therefore he can either hire new labor on full-time basis (for 8-hours day each) at $80 per day or allow over time to existing labor (for 5-hour day each) which will cost $ 110 per day. The contractor wants to limit his extra payment to $ 1000 per day and utilize no more than 20 laborers (either fulltime or part-time) because of limited supervision.

He estimates that new labor employed will generate

$30 per day as profit while an overtime worker will generate $50 per day. Develop an integer optimization model and solve it to aid the building contractor in deciding optimal labor mix.