please put in word document ...please make sure you show enough work to justify your answers. Final...

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please put in word document ...please make sure you show enough work to justify your answers. Final answers without any work shown are not acceptable. MBA 540 Homework Set 2 Question 1. 30 points, each part is worth 5 points.  We have the following information about weekly demand for ai6 cell phones at a Best Purchase store: 	Average weekly demand: 	300 phones 	Standard deviation of weekly demand: 	50 phones 	Order lead time: 	2 weeks 	Standard deviation of order lead time: 	1.5 weeks  	Item cost: 	$600 per phone 	Cost to place an order: 	$100 per order 	Yearly holding cost per phone: 	40% of item cost 	 	 Solution: Some of the data provided above is in weeks while the other is yearly. Therefore converting all of the data to annual time units, the data is as below: a. What is the economic order quantity for this phone? What is the resulting total annual relevant cost? Based on the given data and plugging in the values of D, Co and Ch,  EOQ = Q = SQRT ( 2 x 15600 x 100 / 240) = 114.018 Total Annual Cost TC = (D/Q)*Co + (Q/2)*Ch=(15600/114.018)x100 + (114.018/2)x240 =       				                               = $27,364.21 bbbb. Suppose Best Purchase currently orders a week’s demand at a time (i.e., the order quantity is 300). How does the annual relevant cost of this policy compare with the cost you obtained in part (a)? Show your work. If Best Purchase currently orders a week’s demand => Q = 300. Then Total Annual Cost = TC = (D/Q)*Co + (Q/2)*Ch. Plugging in all D, Co and Ch from the problem description, we get TC = (15600/300) x 100 + (300/2) x 250 = $41,200. The total annual cost is ($41,200 - $27,364.21) = $13835.79 more than when the EOQ was ordered at 114 phones per order when compared to 300 phones per order. This increase in cost is probably because of the holding cost. c.. Suppose the store places an order every time the inventory level drops to 1200. What is the probability of no stock-out achieved under this policy? Since the order is placed every time the inventory level drops to 1200, Reorder Point = 1200. Using the formula Rp = D x L + Safety Stock, we can get the safety stock. Plugging in the values we know in this formula, we get  	Safety Stock = Rp – (DxL) = 1200 – (15600 x 0.038461538) = 600.  Now that we know the safety stock value, we can calculate the probability of no stock-out by using the formula : Safety Stock  = z x sigma-D x √?̅ Solving for z , z = Safety Stock / (sigma-D x √?̅) = 600 / (2600 * √0.038461538) = 1.1766 	 · NORMSDIST(z) NORMSDIST(1.1766) = 88% Therefore, the probability of no stock-out if the reorder point = 1200 is 88%  	 d. Now assume that the store wants to achieve a probability of no stock-out of 99% (z=2.33). What is the new reorder point for the phone? How much of the reorder point consists of safety stock? Calculating for safety stock using Safety Stock  = z x sigma-D x √?̅,  Safety Stock  = 2.33 x 2600 x √0.038461538 = 1188.07  Re-order point to get 99% probability of no stock-out using RP = (DxL)+SafetyStock => RP = (15600 x 0.038461538) + 1188.07 = 1788.07. Therefore the new re-order point to achieve 99% probability of no stock-out = 1788.07. The safety stock is (1188.07/1788.07) 66% of the re-order point. 	 e. Using the economic order quantity from part (a) and the safety stock level from part (d), compute the annual inventory holding cost this store incurs.e.  Total annual cost = TC = (D/Q)*Co + (Q/2+safety stock)*Ch The annual Holding cost from the anove Equation  = (Q/2+safety stock)*Ch   			=  ( 114.01/2 + 1188.07 ) x 240 = $298,819.28  · Annual Holding Costs = $298,819.28   f. Because electronics becomes obsolete so quickly, Best Purchase is thinking about raising holding cost from 40% of item cost to a higher percentage. What will be the impact on the economic order quantity? Briefly explain your answer. Increase in the annual holding cost will reduce the EOQ. As the holding cost increases, to retain the economic benefit to the company, ordering lesser inventory on each order is the right thing to do. For example: The holding cost as per the problem description is 40% of the item cost. At this price, the EOQ in 1A is 114.01 units. If the holding cost is increased to 50%, the EOQ then becomes = Squareroot ( 2 x  15600 x $100) / $300 = 101.98. The new EOQ = 101.98 Question 2. 14 points, 7 points for each part SkiForever is planning orders for its 2022 winter catalog. One order will be placed at their supplier nine months ahead of the selling season. The demand forecast for one of the jackets is normally distributed with mean 4000 and standard deviation 1200. The company plans to sell the jackets at a price of $300. SkiForever pays their supplier $150 per jacket and unsold jackets will be moved to the outlet store at the end of the selling season and will be priced at $100. It is assumed that at that price all remaining jackets will sell. It costs $20 to hold a jacket in inventory until the end of the season and move it to the outlet store.  Solution: a. How many jackets should SkiForever order? The number of jacket to be ordered can be calculated by the formula  Q = D+z*sigma-D. Based on the data, D = 4000; sigma-D = 1200. z can be calculated by NORMSINV(F(Q*)).  F(Q*) = Cu/(Cu+Co).  Cu (Understocking cost) = p – c = $300 - $150  = $150 Co (Overstocking cost) = c – s. Here salvage cost is $100. However, there is a holding cost of $20 for each item. Therefore, the salvage cost (s) = $100 - $20 = $80. Therefore Co = $150 - $80 = $70 F(Q*) = Cu / (Cu + Co) = $150 / ($150 + $70) = 0

Subhanbasha · Accepted Answer

MBA 540 Homework Set 2
Question 1:
a. The economic order quantity (EOQ) can be calculated using the formula:
EOQ = sqrt((2 * demand per year * order cost) / holding cost per unit)
where demand per year = 52 * average weekly demand = 1,560 bags order cost = $20 holding cost per unit = 30% of $25 = $7.50
By substituting the values we will get
EOQ = sqrt((2 * 1560 * 20) / 7.5) = 128.7
Therefore, the store should order 128 bags each time to minimize its relevant costs. The total annual relevant cost can be computed by adding the ordering cost of annual  and holding cost of annual:
Annual ordering cost = (demand per year / EOQ) * order cost = (1560 / 128.7) * 20 = $243.15 Annual holding cost = (EOQ / 2) * holding cost per unit = (128.7 / 2) * 7.5 = $483.38
Total relevant cost = ordering cost annual + holding cost annual = $726.53
b. The annual relevant cost of the current policy of ordering 100 bags at a time can be computed using the same formula as in part (a):
Annual ordering cost = (demand per year / order quantity) * order cost = (1560 / 100) * 20 = $312 Annual holding cost = (order quantity / 2) * holding cost per unit = (100 / 2) * 7.5 = $375
Total relevant cost = ordering cost annual + holding cost annual = $687
Comparing this with the total annual relevant cost obtained in part (a), we can see that the current policy of ordering 100 bags at a time is less optimal.
c. The store places an order every time the inventory level drops to 75 bags, which means that the maximum inventory level is 75 + EOQ = 203.7 bags. The probability of no stock-out can be calculated using the normal distribution:
Probability of no stock-out = P(z > (lead time demand - inventory level) / lead time demand standard deviation)
where lead time demand = average weekly demand * lead time = 30 * 2 = 60 bags lead time demand standard deviation = standard deviation of weekly demand * sqrt(lead time) = 5 * sqrt(2) = 7.07 bags z = (lead time demand - inventory level) / lead time demand standard deviation = (60 - 203.7) / 7.07 = -21.5
Using a standard normal distribution table or a calculator, we find that the probability of no stock-out is essentially zero.
d. To achieve a probability of no stock-out of 95%, the store needs to set the reorder point at the demand during lead time plus the safety stock
Safety stock = z * lead time demand standard deviation
where z = 1.645 (corresponding to a 95% service level)
Reorder point = lead time demand + safety stock = 60 + 1.645 * 7.07 = 71.6
Therefore, the store should reorder when the inventory level drops to 71.6 bags. The safety stock is 1.645 * 7.07 = 11.63 bags.
e. The annual inventory holding cost with the EOQ from part (a) and the safety stock level from part (d) can be calculated as: Holding cost = (111.39 + 5.23) / 2 x $7.5 = $842.59
f. If the holding cost per unit per year is increased, the EOQ will decrease. This is because a higher holding cost per unit per year will increase the cost of carrying inventory, making it more expensive to order larger quantities. As a result, the optimal order quantity will decrease to balance the cost of ordering against the cost of holding inventory.

MBA 540 Homework Set 2Question 1. 30 points, each part is worth 5 points. We have the following information about weekly demand for ai6 cell phones at a Best Purchase store:Average weekly...

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