PLEASE EXPLAIN STEP BY STEP AND DRAW DECISION TREE ! THANK YOU SO MUCH

The Hit-and-Miss Manufacturing Company produces items that have a probability p of being defective. These items are produced in lots of 100 . Past experience indicates that p for an entire lot is either 0.05 or 0.4. Furthermore, in 90.0 percent of the lots produced, p equals 0.05 (so p equals 0.4 in 10.0 percent of the lots). These items are then used in an assembly, and ultimately their quality is determined before the final assembly leaves the plant. Initially the company can either screen each item in a lot at a cost of $10 per item and replace defective items or use the items directly without screening. If the latter action is chosen, the cost of rework is ultimately $100 per defective item. Because screening requires scheduling of inspectors and equipment, the decision to screen or not screen must be made 2 days before the screening is to take place. However, one item can be taken from the lot and sent to a laboratory for inspection, and its quality (defective or nondefective) can be reported before the screeno screen decision must be made. The cost of this initial inspection is $20. (a) Find the optimal policy that minimizes the expected cost of manufacturing (b) Compute EVPI (c) Compute EVE Solution: (a) Define events: G= lot is good B= lot is bad ND= item is nondefective D= item is defective Expected cost without testing =$850.0 Optimal decision without testing = Do not screen lots P(G)=0.9,P(B)=0.1P(DG)=0.05,P(NDG)=0.95P(DB)=0.4,P(NDB)=0.6P(D)=0.085,P(ND)=0.915P(GD)=0.529,P(BD)=0.471P(GND)=0.934,P(BND)=0.066 Cost after testing non-defective =$751.0; If tested item is nondefective, then do not screen the lot