A shoe manufacturer in Vietnam needs to decide whether to specialize in women’s or children’s shoes in order to maximize its profit. It can make $70 with one pair of shoes for women and $50 with children’s shoes. Women’s shoes need 3 hours of manufacturing time and 2 hours of polishing, whereas for children this time is 4 hours and 1 hour, respectively. The company has only 2,400 hours of manufacturing time and 1,000 hours of polishing time available daily.
There are other constraints the company needs to consider before deciding the perfect allocation. It knows that their contractors won’t buy more than 450 children shoes per day. In addition, for contractual reasons, it needs to have a daily output of women’s shoes.
Write the linear programming model of this problem