Table 13.4: PA 13-3 Montanso sells genetically modified seed to farmers. It... U

Question

Table 13.4:

PA 13-3 Montanso sells genetically modified seed to farmers. It... Use Table 13.4. Montanso sells genetically modified seed to farmers. It needs to decide how much seed to put into a warehouse to serve demand for the next growing season. It will make one quantity decision. It costs Montanso $8 to make each kilogram (kg) of seed. It sells each kg for $45. If Montanso has more seed than demanded by the local farmers, the remaining seed is sent overseas. Unfortunately, only $3 per kg is earned from the overseas market (but this is better than destroying the seed because it cannot be stored until next year). If demand exceeds its quantity, then the sales are lost the farmers go to another supplier. As a forecast for demand, Montanso will use a normal distribution with a mean of 300,000 and a standard deviation of 100,000. If a part of the question specifies whether to use Table 13.4, or to use Excel, then credit for a correct answer will depend on using the specified method. How many kilograms should Montanso place in the warehouse before a. 420,000 the growing season? Use Table 13.4 and round-up rule. If Montanso put 400,000 kgs in the warehouse, what is its expected Table 13.4 and round-up rule. How many kilograms should Montanso place in the warehouse to greater than 10%? Use Table 13.4 and round-up rule. b. revenue (include both domestic revenue and overseas revenue)? Use c. minimize inventory while ensuring that the stockout probability is no d. What is maximum profit for this seed?

Explanation / Answer

This is a case of newsvendor problem where a newsvendor has to decide how many papers to buy each day.

If too many, he is left with unsold papers that have no value;
If too few, he has lost the opportunity of making a higher profit.

Let us see the data

Part A

Cost = 8$

Proce = 45$

Profit = 37$

Marginal cost with underestimation of demand = 37$ (Cu)
Marginal cost by overestimating demand = 8-3 = 5$ (Co)

Optimal occurs at a point when the expected benefit of an extra would be less than the expected cost for the item.
Expected marginal cost equation:
P(Co) (1-P)(Cu) or

P<= Cu/(Co+Cu)

P<= 37/42 = .8809

As per above table Z value should be around 1.19 which can be rounded upto 1.2

Stock = Mean demand + Z* SD

Stock = 300,000+ 1.2*100,000 = 420,000

Part C - 90% service level

P<= .9

Z score for P=.9 = 1.3

Stock = 300000 + 1.3*100000= 430,000

Part B

if Stock = 400,000 kg

400000 = 300000 + Z*100000

Z= 1

In the table P value for Z= 1 is

P = .8413

Stockout probability = 1- P = .158655 = 15.8655%

Expected lost sales = SD * P = 100,000*.158655 = 15,865 kgs

Expected sales = Mean sales - expected lost sales = 300,000- 15,865 = 284,135 kgs

Expected profit = (profit* Expected sales) - (Overstock cost * Expected left over inventory )

= 37*284,135 - 5 * (400,000-284,135) = 9,933,670$

Part D. Maximum profit

Maximum profit happens when stock = 420,000

P = .8809 (As calculated in part A)

Stockout probability = 1-.8809 = .119 = 11.9%

Expected lost sales = SD * P = 100,000*.119 = 11,900 kgs

Expected sales = Mean sales - expected lost sales = 300,000- 11,900 = 288,100 kgs

Expected profit = (profit* Expected sales) - (Overstock cost * Expected left over inventory )

= 37*288,100- 5 * (420,000-288,100) = 10,000,200$

Hope it helps! Please feel free to comment in case of any questions.

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