The accompanying figure shows the decision tree of an operations manager who is considering a new production technique. ER represents his expected return (in thousand $) from the new technique. If he does not adopt the technique his expected return would be zero. The probabilities of the technique being a success or a failure are .7 and .3 respectively. Compute the expected return (in thousand $) from the adoption of the new production technique.
A) $8,400
B) $1,000
C) -$2,000
D) $7,200
E) $8,000

Question

The accompanying figure shows the decision tree of an operations manager who is considering a new production technique. ER represents his expected return (in thousand $) from the new technique. If he does not adopt the technique his expected return would be zero. The probabilities of the technique being a success or a failure are .7 and .3 respectively. Compute the expected return (in thousand $) from the adoption of the new production technique. 
A) $8,400 
B) $1,000 
C) -$2,000 
D) $7,200 
E) $8,000

Quizplus · Accepted Answer

To compute the expected return, we first calculate the expected value of ER if the technique is a success, and the expected value of ER if the technique fails:
Expected value if successful: $12,000 (0.7) = $8,400
Expected value if failure: $0 (0.3) = $0
Then we calculate the overall expected value by adding these two values:
Expected value = $8,400 + $0 = $8,400
Therefore, the best choice is to adopt the new production technique, as it has an expected return of $8,400.

The Accompanying Figure Shows the Decision Tree of an Operations