If a part of the question specifies whether to use Table 13.4, or to use Excel,
ID: 376956 • Letter: I
Question
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.
a.
How many kilograms should Montanso place in the warehouse before the growing season? Use Table 13.4 and round-up rule.
b.
If Montanso put 375000 kgs in the warehouse, what is its expected revenue[CL1] (include both domestic revenue and overseas revenue)? Use Table 13.4 and round-up rule.
c.
How many kilograms should Montanso place in the warehouse to minimize inventory while ensuring that the stockout probability[CL2] is no greater than 1%? Use Table 13.4 and round-up rule.
d.
What is maximum profit for this seed?
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 $47. 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 275000 and a standard deviation of 150000.
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.
a.
How many kilograms should Montanso place in the warehouse before the growing season? Use Table 13.4 and round-up rule.
b.
If Montanso put 375000 kgs in the warehouse, what is its expected revenue[CL1] (include both domestic revenue and overseas revenue)? Use Table 13.4 and round-up rule.
c.
How many kilograms should Montanso place in the warehouse to minimize inventory while ensuring that the stockout probability[CL2] is no greater than 1%? Use Table 13.4 and round-up rule.
d.
What is maximum profit for this seed?
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Explanation / Answer
Given : Mean = 275000
Std deviation = 150000
a) As the profit margins are high, we assume that monsanto will try to fulfill 99% of its demand. Hence, from the table, z-value = 2.4 for f(z) = 0.99
x-bar = mean + z * std deviation
= 275000 + 2.4 * 150000 = 635,000
b) If we consider 99% of 375,000 kgs is sold in domestic revenue and 1% in the overseas market
Expected revenue = 0.99 * 375,000 * 47 + 0.01 * 375,000 * 10 = $17,486,250
c) For 1% value, respective z-value = 3.7 ( value for f(z) = 0.9999 in table)
x-bar = 275000 + 3.7 * 150000 = 830,000
d) Maximum profit would happen if all the seeds produced are solid in domestic market and production is according to highest possible demand.
z-value = 3.8
x-bar = 275000 + 3.8 * 150000 = 845000
Profit earned = 845000 * (47 - 6) = $34,645,000
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