please showing the solving steps

Question 3: Linear Programming Formulation (20 marks) RunaLot is company based out of New Brunswick that produces running shoes. They have a new line that is about to be released and fortunately, they have excess production capacity at three production facilities that can be used to produce the new design. The new design will be available in children's, women's, and men's models that yield profits of $16, $43, and $39 respectively. The facilities with excess production capacity are located in Moncton, Fredericton, and Edmundston and the excess capacity allows them to produce up to 500, 600, 250 pairs of the new design regardless of the models involved. The marketing department forecasts that if available, 200 pairs of the children's shoes, 650 of the women's, and 500 of the men's can be sold. Given the current economic condition, at each facility some employees will need to be laid off if there's excess capacity that is not utilized for the new shoe line. To avoid layoffs if possible, management has decided that the production facilities should use the same percentage of their excess capacity to produce the new line. Management wishes to know how many of each of the models should be produced by each of the production facilities to maximize profit. ONLY FORMULATE - DO NOT SOLVE THE PROBLEM FOR AN OPTIMAL SOLUTION