Answer:
a. The Production Order Quantity is 1,560 units
b. The Maximum inventory is 780 units
c. The Average inventory is 390 units
d. The Total holding cost is $9,360
e. To manage the inventory cost $18,718.97
Step-by-step explanation:
a. According to the given data we have the following:
Annual Production rate = 292,000 units
Daily production rate(p) = Annual production rate / number of days per year = 292,000/365 = 800 units
Demand rate(d) = 400 units per day
Number of days per year = 365
Annual demand(D) = d × number of days per year = 400 × 365 = 146,000 units
Set up cost(S) = $100
Holding cost (H) = $24
Therefore to calculate the Production Order Quantity we have to use the following formula:
production order quantity(Q) = √ {2DS / H [1-(d/p)]}
= √ {(2x146,000x100) /24[1-(400/800)]}
= √ [29,200,000/24(1-0.5) ]
= √ [29,200,000/(24 x 0.5)]
= √ (29,200,000/12)
= √2,433,333.3333
= 1,560 units
b. To calculate the Maximum inventory we use the following formula:
Maximum inventory ( I - max) = (Q/p) (p-d) = (1560/800)(800-400) = 1.95 x 400 = 780 units
c. To calculate the Average inventory we use the following formula:
Average inventory = I-max/2 = 780/2 = 390 units
d. To calculate the Total holding cost we use the following formula:
Total holding cost = [(I-max / 2) H] = (780/2)24 = 390 × 24 = $9,360
e. To calculate What does it cost to manage the inventory we use the following formula:
Total cost = Annual holding cost + Annual setup cost
Annual setup cost = (D/Q) S = (146000/1560)100 = $9,358.97
Therefore, Total cost =$9,360 + $9,358.97
= $18,718.97