Question

A toy manufacturer has three different mechanisms that can be installed in a doll that it sells. The different mechanisms have three different setup costs (overheads) and variable costs and, therefore, the profit from the dolls is dependent on the volume of sales. The anticipated payoffs are as follows.

	Light Demand	Moderate Demand	Heavy Demand
Probability	0.6	0.3	0.1
Wind-up action	$325	$220	$200
Pneumatic action	$200	$380	$350
Electrical action	-$400	$240	$800

1. Develop a decision tree for this situation and indicate the best solution.
2. Calculate expected value of perfect information

Answer 1

ET Demand Actions Light I Moderate Heavy EMU Wind-up $395 $220 $200 $981 Pneumatic $200 L $380 $ 3500 $969 Electrical $-400 $240 $ 800 $ -88 Probability 0.6 0:3 10.11 AMV * E Chrobability X lonponding demand for Yeach Taction EM V => (Probability of demand X Pay off for each action) EMV (For Wind-up Action ) 10.6x325) + (0-3X220) + (0.1X200) 5 281 P

(Date: / 1201, Date : 1 201 EMV (For pneumatic action) » (200X0:6) + (380 x0.3) +(350 X0.12_ => $269 EMV (For Electrical action] => 10.6 x (-400) + (240X0. 3) +(800x0.)). => * $-88 - Payoff Light Demand (0.6) 8325 Moderate Demand (0.3) $220 Heavy Demand (01) $200 an phim Action Pneumatic Action Electrical Light Demand (0:6) $200 Moderate Demant fen3] $380 \ Heavy Demand (0.1) $350 Light Demand (062 $-400 Moderate Demand (0.3) $240 Action Y + Heavy Demand fo.1) $ 800

vaw. 201 Based on highest EMV (Expected values best solution is wind up Action. (b) EVPI = EVw PI - EVwo PI EVP I - Expected Value of Perfect Information EVPI = Expected Value with Pexfect Information - EVwo PI = Expected Value without Perfect Information EVHAPI Cas calculated ) => $281 EVWPI=E (Pop CProbability of each Demond X Coxsponding Highest Payoff) Even PI = (325x0.6)+(380 80.3)+ _=$38800 X0.1) EVPI = EVw PI – E EVwo PI - = $ 389- $281 - $ $108

All the parts have been done as shown.