statistics word problem help

Question

One of Umbrella Corporation's manufacturing plants makes two independent products, X and Y. The cost to make X is $ 0.7 per unit and the cost to make Y is $ 0.1 per unit. There is a monthly fixed cost of $ 2,391 at the plant. Monthly demand for X and Y is random, but it is known that the expected demand for X, E(X), is 2,726 and the expected demand for Y, E(Y), is 1,348.

If C is the total monthly cost to make X and Y, find E(C), to two decimal places. Hint: use the rules of expected value.

Answer 1

Daniella,

 

Let C = cost to make product X + cost to make product Y = 2391+.7X + .1Y

 

Rules of expected value say that if h(x) = A + BX, E(h(x))=A + B* E(X)

So E(C) = 3491+.7*E(X) + .1* E(Y) = 2391+.7*2726+.1*1348=2391+1980.2+134.8=4506.00

 

Hope that helps!