For the following linear programming problems, DO NOT SOLVE. Read each part carefully for what is required. 12. A manufacturer produces and sells three products: A, B, and C. The profit margin for product A is $60, product B is $48, and product C is $35. Product A takes 8 hours to assemble, 6 hours to paint, and 1 ho to inspect. Product B takes 4 hours to assemble, 2 hours to paint, and 1.5 hours to inspect. Product C tal 2 hours to assemble, 1.5 hours to paint, and 0.5 hours to inspect. If the manufacturer has at most 108 hours to assemble, at most 50 hours to paint, and at most 40 hours to inspect and the quantity produced product C must be at most 16, use linear programming to determine how many of each product must be produced to maximize the profit? (a) (1 pts) Define all variables as a complete sentence. (b) (2 pts) State the objective and write the objective function. (c) (4 pts) List all the constraints