Please answer ALL questions 1 through 5. Do not skip any.

Utica Cookware has a production line that can manufacture two different kinds of pressure cookers. The first kind is called Fast Steam or FS. The second kind is called Mass Steam or MS.

Every pressure cooker of these two kinds needs one steam valve for its pressure-cooking function. FS is smaller and requires only 6 pounds of stainless steel for each cooker while MS requires 9 pounds of stainless steel for each. Due to its smaller size, each FS requires only one silicone handle. On the other hand, each MS requires two silicone handles.

The accounting department of the company estimates each FS cooker can bring in $40 as profit while each MS cooker can bring in $50 as profit.

For November 2020, Utica Cookware has 550 steam valves, 800 silicone handles, and 4500 pounds of stainless steel available for its monthly production. Based on the marketing department's feedback, no more than 425 FS cookers can be produced in November 2020. Utica Cookware wants to know how many of these two types of pressure cookers to produce in order to get the highest total profit for November 2020.

1) Formulate this problem as a linear program.

2) Solve the linear program graphically for the optimal solution. Describe the optimal solution.

3) What is the profit generated by using the above optimal solution?

Later Utica Cookware receives an update that 180 pounds of the stainless steel is stolen and must be deducted from its November pressure cooker production plan.

4) Will this update change your optimal solution? Why or why not?

Utica Cookware was notified by its retailors that a new discount policy has been applied to its MS products. While FSs unit profit remains at $40, the revised unit profit for MS now drops to $30.

5) Considering the new discount policy and the earlier stolen 180 pounds of stainless steel, what will be your modified optimal solution and modified profit?