Montanso is a large bio firm that sells genetically modified seed to farmers. Mo
ID: 432686 • Letter: M
Question
Montanso is a large bio firm that sells genetically modified seed to farmers. Montanso needs to decide how much seed to put into a warehouse to serve demand for the next growing season. They will make one quantity decision. It costs Montanso $16 to make each kilogram (kg) of seed. They sell each kg for $90. If they have more seed than demanded by the local farmers, the remaining seed is sent overseas. Unfortunately, they only earn $6 per kg from the overseas market (but this is better than destroying the seed because it cannot be stored until next year). If local demand exceeds their quantity, then the sales are lost – the farmers go to another supplier. As a forecast for local demand they will use a normal distribution with a mean of 300,000 kgs and a standard deviation of 100,000 kgs.
How many kilograms (kgs) of seed should they place in their warehouse before the next growing season to maximize their expected profit?
Explanation / Answer
Following to be noted:
Underage cost = Cu = Price of seed – cost of seed =$90 - $16 =$74
Overage cost = Co = Cost of seed – Savage cost in overseas market = $16 - $6 = $10
Therefore critical ratio = Cu / ( Cu + Co ) = 74 / ( 74 + 10 ) = 74/84 = 0.8809
Critical ratio is the instock probability and thus willhelp to determine optimum order quantity .
Corresponding Z value for ins tock probability = NORMSINV ( 0.8809 ) = 1.1794
Quantity of seeds to be placed in warehouse
= Mean demand + Z value x Standard deviation of demand
= 300,000 + 1.1794 x 100,000
= 300,000 + 117940
= 417940 kg