4. Swan-Turkey are considering building a new shipyard (set-up cost 0.9m). This is a risky busi- ness; suppose orders will either be high (with net operating profit 3m) or low (with net operating profit of only 1m), with equal probability (treat these as one-off returns). Alternatively, they can commission market research (at a cost of 100,000) which will study the market further. Clearly, the consultants will predict either high or low demand for the product. If they are always right in their predictions, is it worth commission-ing the study? Assume that the decision-maker wishes to use a utility function (w) w" with initial wealth w4m. Note that this problem is straightforward, but involves intermediate deci- sions (if you hire the consultant, you have a subsequent decision as to whether to invest or not). Work out optimal decisions at these later points first.