Shams furniture assembles two types of Bed frames for retail business: standard and heavy-duty. The process requires two steps. Step-1 takes 10 minutes for the standard frame and 12 minutes for the heavy-duty. Step-2 takes 4 minutes for the standard frame and 12 minutes for the heavy-duty. The companys labor contract requires that it uses at most 400 labor-hours per week on the Step-1 equipment and at most 280 labor-hours per week on the Step-2 equipment. The profit contributions are $20 for each standard and $35 for each heavy-duty. How many of the two types of bed frames should be made each week to maximize profits? Find the optimal solution using the graphical solution technique. Draw the graph, shade the feasible region, point out the optimal corner, find the coordinates of the optimal corner. Answer the following questions: What is the linear math model for this problem? Show the graph in detail. What is the value of the decision variables What is the value of the objective function Is there any slack or surplus? Where and how much?