Shams furniture assembles two types of Bed frames for retail business: standard and heavy-duty. The process requires two steps. Step-1 takes 10 hours for the standard frame and 12 hours for the heavy-duty. Step-2 takes 4 hours for the standard frame and 12 hours for the heavy-duty. The company's labor contract requires that it uses at most 4000 labor-hours per week on the Step-1 equipment and at most 2800 labor-hours per week on the Step-2 equipment. The profit contributions are $12 for each standard and $26 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:

1. What is the linear math model for this problem?
2. Show the graph in detail.
3. What are the values of the decision variables
4. What is the value of the objective function
5. Is there any slack or surplus? Where and how much?