Probability and Statistics/Operations Research. Please help!!!

Question

Due to local zoning laws, you will only be allowed to build one widget factory this year. You have decided that the only reasonable choices are between a medium-sized factory and a large factory, and in these hard times, demand will either be terrible (5,000 units per year) or weak (12,000 units per year), but you want to be ready for an eventual recovery. It costs $10,000,000 to set up a medium-sized factory to produce up to 50,000 widgets per year. The unit cost of producing one widget in the medium-sized factory is $6,000. It costs $20,000,000 to build a big factory to produce up to 250,000 widgets per year. The unit cost of producing one widget in the big factory is $5000. You can sell widgets for $10,000 each. The important factor not under your control is the demand for widgets. The probability of terrible demand is 75%. The probability of weak demand is 25%. There is a very good industry analyst, but he is not perfect. The probability that he will say demand will be terrible given the case of actual terrible demand is 75%. The probability that he will say demand will be weak given the case of actual weak demand is 90%. Apply Bayes theorem to compute the probability that this analyst will predict terrible demand and the probability that this analyst will predict weak demand.

Answer 1

probability analyst will predict terrible demand = probability he will predict terrible demand given case of terrible demand times probability of terrible demand or .75*.75 plus

probability he will predict terrible demand given weak demand times probability of weak demand  or .25*.25

 

probability that analyst will predict weak demand = probability he will predict weak demand given weak demand times probability of weak demand or .9*.25 plus

probability he will predict weak demand given terrible demand times probability of terrible demand or .1*.75

 

Hope that helps,

Deanna