A manufacturer of personal protective equipment (PPE) is considering to make investment in machinery in anticipation of growing demand, or not investing and losing the opportunity of sales revenue and market share. From her past experience, she estimates that there is about a 30% probability of strong demand growth in the market. If the investment in machinery is made and demand is strong, the manufacturer will realize a payoff of $4 million. If no investment is made under strong demand growth, the manufacturer will still receive a payoff of $800,000 with its existing equipment.

If demand growth is not that strong and the manufacturer has made investment in machinery earlier, the payoff will be -$2 million. However, if no investment has been made earlier, the manufacturer will still expect some moderate payoff of $500,000.

i. For each decision alternative of the manufacturer, compute the expected value and standard deviation of monetary payoff.

ii. Based on expected monetary payoff, recommend the best decision for the manufacturer.

iii. Compute the expected value of perfect information and interpret its meaning.

iv. Under the expected payoff criterion, determine the range of probability values of strong demand growth in which the best decision will remain the same as in (a)(ii)?

v. Suppose the manufacturer decides to consult an expert who provides an opinion about the chance of strong demand for PPE based on a forecasting model of infection rates. From past records, the expert’s predictions on strong growth have been 70% accurate, whereas the predictions for non-significant growth has been 80% accurate. Determine the manufacturer’s best strategy to maximize expected payoff if the expert predicts.