Mr. Norway, a homemade ketchup supplier of famous restaurants in Philadelphia, produces ketchup in a certain number of units at once to save the setup costs as much as possible, due to his small scale. Norway plans to produce their homemade ketchup in batch of 50, 100, 150, 200 units. Using historical data, Norway was able to determine that the probability of selling 50, 100, 150, and 200 units are 0.2, 0.3, 0.4, and 0.1, respectively. The question facing Norway is how many units to produce in the next batch run. The price is $20 per unit, manufacturing cost is $12 per unit, warehousing costs are estimated to be $1 per unit. In addition, Norway pays $50 for quality inspection certificate after each batch produced.

Unfortunately, a homemade ketchup only preserves its highest quality level in a very short period of about one month. If it is not sold after the batch run, the remaining units of ketchup that lose much of their special flavor are sold to local convenient stores at $16 per unit. Furthermore, Norway has guaranteed to his suppliers that there will always be an adequate supply of ketchup at the fixed price. If the ketchup in his inventory does run out, he has agreed to get products from his brothers company at the same price he sells $20 per unit, plus transportation costs of $1 per unit.

a. Develop a decision tree of this problem.

b. What is the best solution?

c. (10 extra points) Determine the expected value of perfect information.

Hint: Be careful in conducting the payoff table. Please be noticed that

** In case supply > demand, there are units that are not demanded from restaurants but can be sold at lower price to local convenience store.

** In case supply < demand, there are units that were not produced to meet all the need, so Norway must outsource at $20 (and $1 logistic cost) and in turn sell to restaurants at same price as before. ** The cost of obtaining quality inspection is per batch produced, not per unit produced