Hi, please solve this question is very important and it difference from others question that have been posted on the web. Mr. Dave, a homemade ketchup supplier of famous restaurants in Washington, produces ketchup in a certain number of units at once to save the setup costs as much as possible, due to his small scale. Dave plans to produce their homemade ketchup in batch of 50, 100, 150, 200 units. Using historical data, Dave 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 Dave 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, Dave 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 $16.5 per unit. Furthermore, Dave 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.

1. Conduct the payoff table

2. Develop a decision tree of this problem. What is the best solution?

3. Determine the expected value of perfect information.