Rider manufactures riding lawn mowers at two plants: one in Erie and one in Buffalo. Production costs at the two facilities differ because of varying labor rates, local property taxes, type of equipment, and capacity. The Erie plant has monthly costs that can be expressed as a function of the number of mowers produced: TCE(X) = 2x²-6x where X is the monthly volume of mowers produced at Erie. The Buffalo plant's monthly production costs are expressed as: TCB(Y)=2Y+80Y where Y is the monthly volume of mowers produced at Buffalo. Manufacturing takes place in three departments: assembly, testing, and finishing. Requirements per unit in each department are shown for each plant as follows: Assembly Hours Required Testing Hours Required Finishing Hours Required Erie 3 2 5 Buffalo 4 1.5 7 Because the plants are a short distance apart, workers can be assigned to either plant on a dynamic basis. Total combined capacity for both plants is as follows: Assembly-45,000 hours Testing-24,000 hours Finishing-75,000 hours Rider's production plan calls for 13,000 total mowers to be produced between the two plants at minimum cost. Develop a mathematical and Excel model to determine the optimal number of mowers to produce at each facility.