Shoe production: full expenditure and a budget cap

To add to its existing inventory of shoes, a footwear company plans to manufacture 20 pairs of sports shoes with a budget of $980. The company manufactures three types of sports shoes: Walkers, Runners and Trainers, whose manufacturing costs per pair are $30, $40 and $50 respectively. Find the possible combinations of the number of pairs of each type of sports shoes that the company can manufacture.4 marks

If the company plans to sell each pair of Walkers, Runners and Trainers at $80, $130 and $150 respectively, how many pairs of each type of sports shoes should the company manufacture in order to maximise profit?2 marks