Micromedia offers computer training seminars on a variety of topics. In the seminars each student works at a personal computer, practicing the particular activity that the instructor is presenting. Micromedia is currently planning a two-day seminar on the use of Microsoft Excel in statistical analysis. The projected fee for the seminar is $575 per student. The cost for the conference room, instructor compensation, lab assistants, and promotion is $8,235. Micromedia rents computers for its seminars at a cost of $135 per computer per day. (a) Develop a model for the total cost (C) to put on the seminar. Let x represent the number of students who enroll in the seminar. C= (b) Develop a model for the total profit (P) if x students enroll in the seminar. P= (c) Micromedia has forecast an enrollment of 40 students for the seminar. How much profit will be earned if their forecast is accurate? P(40)=$ (d) Compute the break-even point. x= Brooklyn Cabinets is a manufacturer of kitchen cabinets. The two cabinetry styles manufactured by Brooklyn are contemporary and farmhouse. Contemporary-style cabinets sell for $110 and farmhouse-style cabinets sell for $120. Each cabinet produced must go through carpentry, painting, and finishing processes. The following table summarizes how much time in each process must be devoted to each style of cabinet. Carpentry costs $15 per hour, painting costs $12 per hour, and finishing costs $18 per hour; and the weekly number of hours available in the processes is 2,800 in carpentry, 1,400 in painting, and 1,400 in finishing. Brooklyn also has a contract that requires the company to supply one of its customers with 550 contemporary cabinets and 600 farmhouse-style cabinets each week. Define x and y as follows. x= the number of contemporary-style cabinets produced each week y= the number of farmhouse-style cabinets produced each week (a) Develop the objective function, assuming that Brooklyn Cabinets wants to maximize the total weekly profit. Max (b) Show the mathematical expression for each of the constraints on the three processes. carpentry painting finishing (c) Show the mathematical expression for each of Brooklyn Cabinets' contractual agreements. contemporary farmhouse