The monthly demand D for a certain product manufactured by U

The monthly demand, D, for a certain product manufactured by Umbrella Corporation has the following probability distribution. d P(D = d) 4,805 0.20 9,915 0.45 2,142 0.35 The cost to make each unit of product is $7.73 plus overhead of $1,039. Thus, total cost can be written as C = 7.73*D + 1,039. 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).

Solution

E(D)=0.2*4,805 + 0.45*9,915 +0.35*2,142 = 6,172.45

For

C=7.73D+ 1,039

E(C) = 7.73*E(D) +1,039

E(C) = 7.73 * 6172.45 +1039 = $ 48,752.0385