Consider a product with a daily demand of 400 units, a setup cost per production run of $100, a holding cost per unit of $24.00, and an annual production rate of 292,000 units. The firm operates and experiences demand 365 days per year. a. What is the Production Order Quantity? (Select] b. What is the max inventory on hand? (Select] c. What is the average inventory? (Select] d. What are the total holding costs? $ (Select] e. What does it cost to manage the inventory?

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

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

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explanation:

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