A toaster manufacturer (FC) has to fulfill a contract to supply a department store chain during...

 

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A toaster manufacturer (FC) has to fulfill a contract to supply a department store chain during the next 6 months the following number of toasters: month 1 month 2 12,000 month 3 month 4 month 5 month 6 9,000 8,000 4,000 10,000 10,000 At the beginning of month 1, FC has 0 workers and 0 inventory. The salary of each worker at FC is $2,500 per month. FC can hire and fire workers at the beginning of each month. The number of hired workers each month cannot exceed 16. The hiring and firing costs of one worker are respectively, $3,000 and $2,200. FC can also require its workers to work overtime. Each full-time worker makes 600 toasters a month (regular time) and up to 160 toasters (overtime). Each toaster costs $15 in raw material. The cost of making a toaster during overtime is $27.5 (raw material plus the overtime cost). Finally, inventory can be carried forward from month to month at a cost of $1.5 per toaster-month. Formulate the problem of minimizing the cost for FC as an LP. Solve the LP model and find the optimal cost and the optimal production plan. Also explicitly answer the following questions: (a) What is the optimal total cost for FC? (b) What is the number of workers at the end of month 67 (c) What is the inventory carried forward from month 5 to month 6? A toaster manufacturer (FC) has to fulfill a contract to supply a department store chain during the next 6 months the following number of toasters: month 1 month 2 12,000 month 3 month 4 month 5 month 6 9,000 8,000 4,000 10,000 10,000 At the beginning of month 1, FC has 0 workers and 0 inventory. The salary of each worker at FC is $2,500 per month. FC can hire and fire workers at the beginning of each month. The number of hired workers each month cannot exceed 16. The hiring and firing costs of one worker are respectively, $3,000 and $2,200. FC can also require its workers to work overtime. Each full-time worker makes 600 toasters a month (regular time) and up to 160 toasters (overtime). Each toaster costs $15 in raw material. The cost of making a toaster during overtime is $27.5 (raw material plus the overtime cost). Finally, inventory can be carried forward from month to month at a cost of $1.5 per toaster-month. Formulate the problem of minimizing the cost for FC as an LP. Solve the LP model and find the optimal cost and the optimal production plan. Also explicitly answer the following questions: (a) What is the optimal total cost for FC? (b) What is the number of workers at the end of month 67 (c) What is the inventory carried forward from month 5 to month 6?

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Answer a Step 1 Assign the full time worker less than or equal to 16 and determine the number of toa... View the full answer