1. Zhen Manufacturing is considering the introduction of a family of new products. Long- term demand for the product group is somewhat predictable, so the manufacturer must be concerned with the risk of choosing a process that is inappropriate. Chen Zhen is VP of operations. He can choose among batch manufacturing or custom manufacturing, or he can invest in group technology. Chen won't be able to forecast demand accurately until after he makes the process choice. Demand will be classified into four compartments: poor, fair, good, and excellent. The table below indicates the payoffs (profits) associated with each process/demand combination, as well as the probabilities of each long-term demand level. PoOR FAIR GOOD EXCELLENT Probability Batch .2 $1,300,000 .1 .4 .3 -$ 200,000 $ 100,000 -$1,000,000 $1,000,000 $ 300,000 -$ 500,000 $1,200,000 $ 700,000 $ 500,000 $ 800,000 $2,000,000 Custom Group technology a) Based on expected value, what choice offers the greatest gain? b) What would Chen Zhen be willing to pay for a forecast that would accurately determine the level of demand in the future?

EVE Online is a space-based multiplayer game, where players use spaceships to engage in combat, industry, exploration and other activities. Players can design their own ships, incorporating ship systems that affect a range of different critical variables. In combat situations, one such critical variable is ”capacitor recharge rate”: the capacitor stores energy used for activating both offensive and defensive ship systems. A spaceship that runs out of energy rarely survives for long. The capacitor recharge rate varies with how full the capacitor is currently. The recharge rate is determined by the differential equation dC/dt = 10 M/T [√(C/M) − C/M] where M is the capacitor’s overall capacity for holding energy (measured in gigajoules, GJ), and T is the time (measured in seconds, s) taken to recharge from zero to a standardised fraction of M. a) Using Rolle’s theorem, infer that there is a maximum value for dC/dt for some C ∈ (0, M). b) Treating M and T as constant, show that dC/dt is at…

answer D & E ONLY

ABC Corporation is considering three options for managing its data processing operation: continuing with its own staff, hiring an outside vendor to do the management (referred to as outsourcing), or using a combination of its own staff and an outside vendor. The profit of the operations depends on future demand. The annual profit of each option (in thousands of dollars) and for each state of demand is summarized in the following table: Staffing Options Own Staff Outside Vendor Combination High 650 900 800 Demand Medium 650 600 650 Low 600 300 400 1. If the manager of ABC Corporation is optimistic, which staffing option will he/she choose? 2. If the manager of ABC Corporation is conservative, which staffing option will he/she choose? 3. Suppose the probabilities of high, medium, and low demand are 40%, 10% and 50%, respectively. Using the expected value approach, which staffing option should the manager choose? 4. What is the expected value of perfect information?