The next growing season to maximize their expected profit

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Reference no: EM132193611

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.

1. Newsvendor Quantity: How many kilograms (kgs) of seed should they place in their warehouse before the next growing season to maximize their expected profit?

(i) A senior executive at the company asks the following, “Suppose we were to place 500,000 kilograms in this warehouse. What is the probability that our total revenue will be greater than $35,000,000?” This question is concerned with actual revenue values, not expected revenue or the average revenue. Don’t forget that total revenue comes from both local sales and overseas sales, which depend on the realized value of local demand and the supply of seeds placed in the warehouse. Furthermore, you are concerned with revenue and not profit, so you can ignore costs. [Hint: Write the total revenue as a function of the realized local demand value and the quantity placed in the warehouse.]

(ii) Suppose Montanso places 400,000 kilograms in their warehouse. Calculate the expected local sales of seed and the expected overseas sales of seed. Would these sales values increase, decrease, or remain unchanged if the standard deviation of demand decreases?

Reference no: EM132193611

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