Use Table 13.4 Montanso sells genetically modified seed to farmers. It needs to
ID: 329212 • Letter: U
Question
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 $6 to make each kilogram (kg) of seed. It sells each kg for $43. If Montanso has more seed than demanded by the local farmers, the remaining seed is sent overseas. Unfortunately, only $4 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 350000 and a standard deviation of 75000 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 the growing season? Use Table 13.4 and round-up rule If Montanso put 425000 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 5%? 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
a) Underage cost, Cu = selling price - cost = 43-6 = $ 37
Overage cost, Co = cost - overseas sale price = 6 - 4 = $ 2
Critical ratio, F(z) = Cu/(Cu+Co) = 37/(37+2) = 0.9487
Use table 13.4 and look for F(z) = 0.9487 or higher (round-up rule). Corresponding z-statistic = 1.7
Optimal stock (kilograms) to keep in warehouse before the growing season = mean + z * Std dev
= 350000 + 1.7*75000
= 477,500
b) z-statistic = (425000 - 350000)/75000 = 1
I(z) = 1.0833 (taken from table 13.4)
Expected leftover inventory = s*I(z) = 75000*1.0833 = 81249
Expected Sales = Stock - Expected leftover = 425000 - 81249 = 343751
Expected revenue = expected sales * domestic sales price + expected leftover inventory * overseas sales price
= 343751 * 43 + 81249 * 4
= $ 15,106,289
c) For stockout probability to be less than 5%, F(z) = 0.95
z-statistic = 1.7 (corresponding to 0.9554 using round-up rule)
Quantity to place in warehouse = 350000 + 1.7*75000 = 477,500
d) Maximum profit = Mean demand * Cu = 350000*37 = $ 12,950,000
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