Q. A workshop is about to install a new machine for stamping and pressing parts for domestic appliances. 3 suppliers have made bids to supply machine. First supplier offers Basic or machine which automatically produces parts of acceptable, but not outstanding quality. Output from machine is variable (depending on material supplied and a variety of settings) but could be 1000 a week (with probability o.1), 2000 a week (with probability 0.7) or 3000 a week. Notional profit for this machine is $4 a unit. Second supplier offers a Super stamp machine which makes higher quality parts. Output from this can be 700 a week (with probability 0.4) or 1000 a week, with a notional profit of $10 a unit. Third supplier offers Switch cover machine which can be set to produce either 1,300 high-quality parts a week at a profit of $6 a unit or 1600 medium-quality parts a week with a profit of $5 a unit.

If machine produces 2000 or more units a week, it is possible to export all production as a single bulk order. n re is a 60% chance of selling for 50% more profit and a 40% chance of selling for 50% less profit. Illustrate what should be d1 to maximize expected profits?