One of Umbrella Corporations manufacturing plants makes two

One of Umbrella Corporation\'s manufacturing plants makes two independent products, X and Y. The cost to make X is $ 0.18 per unit and the cost to make Y is $ 0.34 per unit. There is a monthly fixed cost of $ 4,271 at the plant. Monthly demand for X and Y is random, but it is known that the expected demand for X, E(X), is 1,862 and the expected demand for Y, E(Y), is 1,089.

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

Solution

Let C = X + Y

E(C) = E (X + Y) = E(X) + E(Y) = 1862 +1089 = 2951