Montanso is a large bio firm that sells geneticall modified seed to farmers. They need 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 $8 to make each kilogram of seed. They sell each kg for $45. if they have more seed than demanded by the local (domestic) farmers, the remaining seed is sent overseas. Unfortunately, they only earn $3 per kg from the overseas market (but this is better than destroying the seed because it cannot be stored until next year). If demand exceeds their quantity, then the sales are lost - the farmers go to another supplier. As a forecast for demand they will use a normal distribution with a mean of 300,000 and a standard deviation of 106,000.
a) How many kilograms should they place in this warehouse before the 2011 growing season?
b) Ignoring the analysis in the previous question, how many kilograms should they place in this warehouse if they want to minimize their inventory while ensuring that the stockout probability is no greater than 10%?
c) A senior executive at the company asks the following: "suppose we were to place 500,000 kilograms in this warehouse (leftover inventory). what is the probability that our total revenue will be at least $18,000,000?"
Hint: Don't forget that revenue comes from both domestic sales (demand) and overseas sales for leftover inventory. Furthermore, you are concerned with revenue and not profit, so you can ignore costs. So, write down the revenue as the function of domestic sales (demand). Then figure out what the sales (demand) is for revenue = 18 million. Now calculate the probability of the demand larger than that sales which generates the 18 million revenue.