Reboot, Inc, is a manufacturer of hiking boots. Demand for boots is highly seaso
ID: 441961 • Letter: R
Question
Reboot, Inc, is a manufacturer of hiking boots. Demand for boots is highly seasonal. In particular, the demand in the next year is expected to be 3,000, 4,000, 8,000, and 7,000 pairs of boots in quarters 1, 2, 3, and 4, respectively. With its current production facility, the company can produce at most 6,000 pairs of boots in any quarter. Reboot would like to meet all the expected demand, so it will need to carry inventory to meet demand in later quarters. Each pair of boots sold generates a profit of $20 per pair. Each pair of boots in inventory at the end of a quarter incurs $8 in storage and capital recovery costs. Reboot has 1,000 pairs of boots in inventory at the start of quarter 1. Reboot's top management has given you the assignment of modeling and analyzing what the production schedule should be for the next four quarters. In particular, you are asked to determine how many pairs of boots to produce in each quarter so that you satisfy the demand in each quarter, while doing so, you want to maximize the total annual profit, which is equal to the profit gained from sales minus the inventory costs.Explanation / Answer
Particulars Quarter 1st Quarter 2nd Quarter 3rd Quarter 4th
OPening Goods 1000 NIL NIL 2,000
Demand 3000 4,000 8,000 7,000
_______________________________________________________________
Total boots 4,000 4,000 8,000 9,000
multiply profit * 20 * 20 * 20 * 20
______________________________________________________________
Sales $80,000 $80,000 $160,000 $180,000
Less:
Ending Inventory NIL NIL $16,000 $24,000
_______________________________________________________________
profit $72,000 $80,000 $144,000 $156,000
______________________________________________________________
Notes
Storage Cost= Inventory ending Quarter 3st and 4th having 2,000 and 3,000 respectively so multiplied with $8 as storage cost.
2000 * 8 =$16,000
3,000 * 8 =$24,000
Ending inventory for the 4th quarter:
All quarter needs to produce 6,000 but 3rd quarter produced 8,000 - 6,000= 2000 and 4th quarter 9000 - 6000=3,000 considered as ending inventory.
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