Red Dwarf Toasters needs to produce 1000 of their new “Talking Toaster”. There are three ways this toaster can be produced: manually, semi-automatically, and robotically. Manual assembly requires 1 minute of skilled labor, 40 minutes of unskilled labor, and 3 minutes of assembly room time. The corresponding values for semiautomatic assembly are 4, 30, and 2; while those for robotic assembly are 8, 20, and 4. There are 4500 minutes of skilled labor, 36,000 minutes of unskilled labor, and 2700 minutes of assembly room time available for this product. The total cost for producing manually is $7/toaster; semi-automatically is $8/toaster; and robotically is $8.50/toaster. (a) Formulate the problem of producing 1000 toasters at minimum cost meeting the resource requirements. Clearly define your variables, objective and constraints. (b) The union contract states that the amount of skilled labor time used is at least 10% of the total labor (unskilled plus skilled) time used. Update your formulation in (a) to handle this requirement. (c) Any unused assembly floor time can be rented out at a profit of $0.50/minute. Update your formulation to include this possibility.
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