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 $ 0.41 per unit and the cost to make Y is $ 0.68 per unit. There is a monthly fixed cost of $ 4,719 at the plant. Monthly demand for X and Y is random, but it is known that the variance in demand for X, V(X), is 2,712 and the variance in demand for Y, V(Y), is 2,239.

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

Solution

Total monthly cost (C )=  4,719 +X +Y

var(C) = VAR(X) +VAR(Y) (as we know that X and Y are independent of each othre thus covariance term =0)

var(C) = 2,712 + 2239

= 4951