Johnson, Inc. markets various electronics products. Currently, Alexander is preparing to introduce two new products called FM and the other called TEC. Each product has three components: a base, an electronic cartridge, and a faceplate or top. The same base will be used for both products, but the cartridges and tops are different. All components can be manufactured by the company or purchased from outside suppliers.

Company's Supply Chain Analyst indicates that at least 3,500 FM units and 2,500 TEC units will be needed for the next planning period. However, the manufacturing capacity is limited. All components will need processes from two departments, Department A and Department B. The company has 350 hours of regular manufacturing time in Department A and 280 hours of regular manufacturing time in Department B that can be scheduled for the products. The company's Supply Chain Director indicated that the total manufactured components must be at least half of the total manufactured and purchased components combined. The following table shows the manufacturing times for the components. The manufacturing costs, purchase prices, and manufacturing times are given in the following table:

Manufacturing Purchase Manufacturing Time (Minutes) Component Cost per Unit Cost per Unit Department A Department B Base $11.00 $12.85 1 2 FM Cartridge $43.50 $56.50 3 1.5 TEC Cartridge $43.50 $51.00 2.5 1 FM Top $12.00 $13.75 1 1 TEC Top $13.25 $15.95 1.5 1.5

Determine the number of components to be manufactured and/or purchased in order to minimize the total cost using linear programming method.