You are a data center manager and have been asked by your boss to redesign a telecommunications room in one of your smaller facilities. One element of this redesign you would like to optimize is the rack structure - your goal is to provide the greatest amount of equipment storage (by weight) within the cost constraints of the project. There are two types of storage racks you can choose from. Rack A costs $360 per unit, requires three square feet of floor space, and can support up to 70 pounds of equipment. Rack B costs $900 per unit, requires five square feet of floor space, and can support up to 130 pounds of equipment. Your budget for this aspect of the project is $6,300, though of course you don't have to spend all of it. Additionally, you can allocate at most 45 square feet of floor space to the racks in this room. How many of each type of rack should you buy to maximize the amount of equipment that could be supported?

1. What are your variables for this project? Assign each a letter and describe them in words.

2. What is the objective function you are being asked to maximize? Assign it a variable, define it in words, and provide an equation for it using the variables you defined above.

3. There are four constraints for this problem (hint: one is for the cost of the racks, one is for floor space, and two other 'natural' constraints). Write these four constraints as inequalities.

4. Using a web-based graphing tool like https://www.mathway.com/Graph to develop a graph of these constraints.Your graph should indicate which area is the feasible region of possible solutions.

5. Based on your graph, how many points are possible solutions? Give the coordinates of each of these points and evaluate the objective function at each point.

6. Now we can answer our original problem: how many of each type of rack should you buy to maximize the amount of equipment that this room can support?Also, indicate how much of your original budget you will spend and the amount of floor space these racks will take up in total.