QUESTION 6 STAT The monthly demand D for a certain product

QUESTION 6 - STAT

The monthly demand, D, for a certain product manufactured by Umbrella Corporation has the following probability distribution.

The cost to make each unit of product is $9.88 plus overhead of $1,546. Thus, total cost can be written as C = 9.88*D + 1,546. Find E(C), the expected total cost per month to the nearest dollar, using the rules of expected value. Hint: you first have to find E(D).

ANSWER: ____________

Solution

Consider the table:      
      
d   P(d)   d P(d)
6988   0.2   1397.6
9178   0.45   4130.1
4269   0.35   1494.15

Thus,

E(D) = Sum (d P(d)) = 7021.85

Thus,

E(X) = 9.88*E(D) + 1546 = 9.88*7021.85 + 1546 = 70921.878 [ANSWER]