A firm is planning its production for the next 10 weeks. The demand has been est
ID: 2458907 • Letter: A
Question
A firm is planning its production for the next 10 weeks. The demand has been estimated according to the following:
The firm runs the production in batches. Starting a new batch involves a change-over which is estimated to cost 792 dollars per batch. During the weekend the facility is shut-down for maintenance, so the first batch of the week incurs the same setup cost as any other batch.
The maximum capacity of production is 25,000 units per week. Units produced in one week incur no holding cost if they are sold during that week. Holding them for future weeks, however, incurs a holding cost of 0.1 dollars per unit per week.
If the firm was to implement the cost-minimizing production plan for the units, what is the total cost for producing the 10 week's demand above?
** Note, I tried $7920 and it is incorrect.
Week 1 2 3 4 5 6 7 8 9 10 Demand 3,000 2,400 2,200 2,500 2,600 2,300 2,000 2,100 3,000 2,600Explanation / Answer
The total demand in 10 weeks = 24700 units
The maximum production capacity is 25000 per week
If we manufacture the demanded units each week, then the cost would be $792*10 = $7920
If we produce all the units in one week, then this cost of $7920 would not be incurred and we just have to incur the holding cost of $0.1 per unit per week.
So, we produce 24700 units in first week and would hold the rest 24700 -3000 i.e 21700 units for the coming weeks.
The costs that we would incure = 21700*$0.1 = $2170
This would be the total cost for producing the 10 week's demand above.
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