Solada Fox sells fruit from her three farms. Apples are 2 a case, peaches are 5 a case, and apri

step 1 To find the total income of the three fruit farms, you want to multiply by the matrix of the num

Solada Fox sells fruit from her three farms. Apples are 2 a...

Solada Fox sells fruit from her three farms. Apples are $\$22$ a case, peaches are $\$25$ a case, and apricots are $\$18$ a case. Find the total income of the three fruit farms expressed as a matrix. $$\begin{array}{|c|c|c|c|} \hline \text { Farm } & \text { Apples } & \text { Peaches } & \text { Apricots } \\ \hline 1 & 290 & 165 & 210 \\ \hline 2 & 175 & 240 & 190 \\ \hline 3 & 110 & 75 & 0 \\ \hline \end{array}$$

Solada Fox sells fruit from her three farms. Apples are $\$22$ a case, peaches are $\$25$ a case, and apricots are $\$18$ a case.
Find the total income of the three fruit farms expressed as a matrix.

$$\begin{array}{|c|c|c|c|}
\hline \text { Farm } & \text { Apples } & \text { Peaches } & \text { Apricots } \\
\hline 1 & 290 & 165 & 210 \\
\hline 2 & 175 & 240 & 190 \\
\hline 3 & 110 & 75 & 0 \\
\hline
\end{array}$$

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Key Concepts

Matrix Representation

Matrix representation is a method of organizing data into a structured, rectangular array of numbers arranged in rows and columns. This format is particularly useful in situations where multiple related quantities need to be manipulated simultaneously, such as representing the quantities of different fruits across several farms.

Matrix Multiplication

Matrix multiplication is an operation that combines two matrices to produce a new matrix, where each element is computed as the sum of products of corresponding entries from rows of the first matrix and columns of the second. In revenue calculations, multiplying a quantity matrix by a price vector aggregates individual sales into total incomes for each farm.

Dot Product

The dot product is a specific case of matrix multiplication between a row vector and a column vector. It results in a single number obtained by multiplying corresponding entries and summing the results. In economic contexts, the dot product of a set of quantities with corresponding prices yields the total income from those items.

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