I need help with 6-4. The reference question 2 is also attached 6-4Suppose that

Question

I need help with 6-4. The reference question 2 is also attached

6-4Suppose that the store in Probiem 6-2 can backorder Malabug when it is out of stock. But since most customers are simply itching to go backpacking and may havie to delay their departure to wait to purchase the repellent, there is a penalty of $10 per year in lost goodwill for every bottle short. (a) Determine the optimal order quantity, inventory level, and time between orders. What proportion of the time is Malabug out of stock? Compute the total annual relevant inventory cost of the policy you found in (a). Is this cost larger or smaller than your answer to Problem 6-2(c)? Do you think the same conclusion would be reached if the annual shortage penalty were $1,000 per bottle? (b)

Explanation / Answer

Demand D = 5000 unit
Ordering cost A = $5
Inventory carrying cost h = $3.50

a) EOQ = SQRT(2AD/h) = SQRT(2*5*5000/3.50) = 119.53 = 120 units
b) Annual consumption is 5000 units
So, 120 units will last 120*365/5000 days = 8.76 days
No. of orders placed in 1 year = 5000/120 = 41.67
i.e. 42 orders per year

c) As a result of lower interest rate, icc becomes 1.80
So, new h = $1.80
EOQ = SQRT(2AD/h) = SQRT(2*5*5000/1.80) = 166.67
i.e. new EOQ = 167
No. of orders per year = 5000/167 = 29.94 i.e 30 orders per year

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