A toy manufacturer makes stuffed kittens and puppies which have relatively lifelike motions. There are three different mechanisms which can be installed in these "pets." These toys will sell for the same price regardless of the mechanism installed, but each mechanism has its own variable cost and setup cost. Profit, therefore, is dependent upon the choice of mechanism and upon the level of demand. The manufacturer has in hand a forecast of demand that suggests a 0.2 probability of light demand, a 0.45 probability of moderate demand, and a probability of 0.35 of heavy demand. Payoffs for each mechanism-demand combination appear in the table below.
$$\begin{array} { | l | c | c | c | }
\hline \text { Demand } & \text { Wind-up action } & \text { Pneumatic action } & \text { Electronic action } \
\hline \text { Light } & \$ 250,000 & \$ 90,000 & - \$ 100,000 \
\hline \text { Moderate } & 400,000 & 440,000 & 400,000 \
\hline \text { Heavy } & 650,000 & 740,000 & 780,000 \
\hline
\end{array}$$ Construct the appropriate decision tree to analyse this problem. Use standard symbols for the tree. Analyse the tree to select the optimal decision for the manufacturer.

Question

A toy manufacturer makes stuffed kittens and puppies which have relatively lifelike motions. There are three different mechanisms which can be installed in these "pets." These toys will sell for the same price regardless of the mechanism installed, but each mechanism has its own variable cost and setup cost. Profit, therefore, is dependent upon the choice of mechanism and upon the level of demand. The manufacturer has in hand a forecast of demand that suggests a 0.2 probability of light demand, a 0.45 probability of moderate demand, and a probability of 0.35 of heavy demand. Payoffs for each mechanism-demand combination appear in the table below.
 $$\begin{array} { | l | c | c | c | } 
\hline \text { Demand } & \text { Wind-up action } & \text { Pneumatic action } & \text { Electronic action } \
\hline \text { Light } & \$ 250,000 & \$ 90,000 & - \$ 100,000 \
\hline \text { Moderate } & 400,000 & 440,000 & 400,000 \
\hline \text { Heavy } & 650,000 & 740,000 & 780,000 \
\hline
\end{array}$$ Construct the appropriate decision tree to analyse this problem. Use standard symbols for the tree. Analyse the tree to select the optimal decision for the manufacturer.

Quizplus · Accepted Answer

The Answer of A toy manufacturer makes stuffed kittens and puppies which have relatively lifelike motions. There are three different mechanisms which can be installed in these "pets." These toys will sell for the same price regardless of the mechanism installed, but each mechanism has its own variable cost and setup cost. Profit, therefore, is dependent upon the choice of mechanism and upon the level of demand. The manufacturer has in hand a forecast of demand that suggests a 0.2 probability of light demand, a 0.45 probability of moderate demand, and a probability of 0.35 of heavy demand. Payoffs for each mechanism-demand combination appear in the table below.
 $$\begin{array} { | l | c | c | c | } 
\hline \text { Demand } & \text { Wind-up action } & \text { Pneumatic action } & \text { Electronic action } \
\hline \text { Light } & \$ 250,000 & \$ 90,000 & - \$ 100,000 \
\hline \text { Moderate } & 400,000 & 440,000 & 400,000 \
\hline \text { Heavy } & 650,000 & 740,000 & 780,000 \
\hline
\end{array}$$ Construct the appropriate decision tree to analyse this problem. Use standard symbols for the tree. Analyse the tree to select the optimal decision for the manufacturer.

A Toy Manufacturer Makes Stuffed Kittens and Puppies Which Have