A furniture company makes bookshelves and desks. Each shelf requires 2 hours for carpentry work and 1 hour for painting whereas each desk requires 3 hours for carpentry work and 4 hours for painting. The company has a maximum of 60 hours and 40 hours of carpentry A work and for painting, in turn, each week. If they make a profit of $15 per shelf and $40 per desk, how many shelves and desks should they make? what would the x and y variables be, what is the objective function, the constraints, and the vertices?

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