1. A petrochemical company must decide whether to fill a specialty order for one of its customers. Its cost (and therefore profit) depends on the quality of the raw material it has on hand to make the chemical. The firm expects to earn $80,000 from the order if the material is high quality (H) but will lose $50,000 if it is low quality (L). The firm's engineers estimate these probabilities to be 35% and 65% respectively. Before making its decision, the firm can test the material with one of two outcomes, "favorable" or "unfavorable." A favorable test increases the chance of H to 41%, while an unfavorable result reduces it to 29%. The likelihood of a favorable test is 50%.
2. Does it make sense to fill the special order without the test? [3]
3. Draw decision tree and decide if it make sense to fill the special order with the test.[9]
4. Determine the expected value of this test.[3]