Roedel electronics produces tablet computer accessories, including integrated keyboard tablet stands to connect a keyboard to a tablet device while optimizing the viewing angle of the screen. roedel produces two sizes of tablet stands: large and small. each size uses the same keyboard attachment, but the stand consists of two different pieces, a top flap and a vertical stand that differ by size. thus, a completed integrated keyboard tablet stand consist of 3 subassemblies: a keyboard, a top flap and a vertical stand. roedel’s sales forecast indicates that 7000 small integrated keyboard tablet stands and 5000 large integrated keyboard tablet stands will be needed to satisfy demand during the upcoming christmas season. because only 500 hours of in-house manufacturing time are available, roedel is considering purchasing some, or all, of the subassemblies from outside suppliers. if roedel manufactures a subassembly in-house, it incurs a fixed setup cost as well as a variable manufacturing cost. the following table shows the setup cost, the manufacturing time per subassembly, the manufacturing cost per subassembly and the cost to purchase each of the subassemblies from an outside supplier: subassembly setup cost ($) manufacturing time /unit (min) manufacturing cost/unit (s) purchase cost/unit ($) keyboard 1000 0.9 0.40 0.65 small top flap 1200 2.2 2.90 3.45 large top flap 1900 3.0 3.15 3.00 small vertical stand 1500 0.8 0.30 0.50 large vertical stand 1500 1.0 0.55 0.70 a) formulate a linear program to solve this problem. clearly define all variables.