The Johnson Ladder Manufacturing company is located in Johnson City TN. The company assembles fiberglass stepladders and receives plastic tops from two sources. One source is located in Detroit MI and the other in Louisville KY. Let x = the number of products received from Detroit and y = the number of units received from Louisville. a. Write an expression for the total number of units received by the plant in Johnson City. b. Shipments from Detroit cost $0.30 per unit and shipments from Louisville cost $0.35. Develop an objective function representing the total cost of shipments to Johnson City. c. Assuming that the monthly demand for tops is at most 6,000 units, develop a constraint that requires 6,000 to be shipped to Johnson City. d. No more than 3,500 units can be shipped from Detroit and 4,000 can be shipped from Louisville in a month. Develop constraints to model the situation. e. Negative amounts cannot be shipped. What constraints would eliminate this possibility? f. Combine the objective function and constraints and develop a mathematical model for satisfying the demand at Johnson City at minimum cost. Note: you do not need to solve it just write them out. This part