A shoe manufacturer in Vietnam needs to decide whether to specialize in women's shoes or children's shoes to maximize its profits. A pair of shoes for women can earn $ 70, children's shoes for $ 50. While 3 hours of production time and 2 hours of polishing are carried out in women's shoes, this period is 4 hours and 1 hour respectively in children. The company has a daily production time of only 2,400 hours and a polishing time of 1,000 hours.

There are other restrictions that the company must consider before deciding on the perfect distribution. He knows his contractors won't buy more than 450 children's shoes a day. In addition, due to contractual reasons, there must be a daily ladies' shoe exit.

Write down the linear programming model of this problem.