Question

The Alliance Corp. expects to sell the following number of units of copper cables at the prices indicated, under three different scenarios in the economy. The probability of each outcome is indicated. What is the expected value of the total sales projection?

Outcome	Probability	Units	Price
A	0.70	225	$20
B	0.10	370	35
C	0.20	510	45

Short answer

The total sales value projection of the company is $9,035.

Step-by-step solution

Expected sales value of A

$\begin{array}{rcl}\mathrm{Expected}\mathrm{sales}& =& \mathrm{Units}\mathrm{sold}\times \mathrm{Unit}\mathrm{price}\times \mathrm{Probability}\\ & =& 225\times \$20\times 0.70\\ & =& \$3,150\end{array}$

Expected sales value of B

$\begin{array}{rcl}\mathrm{Expected}\mathrm{sales}& =& \mathrm{Units}\mathrm{sold}\times \mathrm{Unit}\mathrm{price}\times \mathrm{Probability}\\ & =& 370\times \$35\times 0.10\\ & =& \$1,295\end{array}$

Expected sales value of C

$\begin{array}{rcl}\mathrm{Expected}\mathrm{sales}& =& \mathrm{Units}\mathrm{sold}\times \mathrm{Unit}\mathrm{price}\times \mathrm{Probability}\\ & =& 510\times \$45\times 0.20\\ & =& \$4,590\end{array}$

Expected total sales value projection of the Alliance Corp.

$\begin{array}{rcl}\mathrm{Expected}\mathrm{total}\mathrm{sales}\mathrm{value}& =& \mathrm{Expected}\mathrm{sales}\mathrm{of}\mathrm{A}+\mathrm{Expected}\mathrm{sales}\mathrm{of}\mathrm{B}+\mathrm{Expected}\mathrm{sales}\mathrm{of}\mathrm{C}\\ & =& \$3,150+\$1,295+\$4,590\\ & =& \$9,035\end{array}$