Messy LP Problem: Mr. Smith has a factory that makes alarm clock, radio, and alarm clock with radio that uses similar components. Alarm clocks can be sold for about \$5; radios can be sold for about \$3; and alarm clock with radio can be sold for $7. The requirement for each product is listed as follows: Mr. Smith has 4,000 displays at a cost of $0.55 each, 3,000 cases at $0.75 each units, 3,500 counters at $0.10 each, and 2,500 receiver at \$0.6. How should Mr. Smith manage this production to maximize the profit? a. Provide the linear programming formulation. (Submit a MS Word document for this part of the question or a scanned PDF file with all of the equations) b. Solve this problem and provide the sensitivity report (Submit an Excel file for this part of the question) c. In the Excel file (or the MS Word document) indicate if a constraint has a slack, a surplus, or a inding constraint. Identify any resource that you like to change. Explain your reasoning