Answer to Question #304054 in Linear Algebra for Alemante

Question

1. Agriculture A fruit grower raises two crops. apples and peaches. Each of these crops is sent to three different outlets for sale. These outlets are The Farmer's Market. The Fruit Stand, and The Fruit Farm. The numbers of bushels of apples sent to the three outlets are 125,100. and 75. respectively. The numbers of bushels of peaches sent to the three outlets are 100. 175. and 125. respectively. The profit per bushel for apples is$3.50 and the profit per bushel for peaches is $6.00. (a) Write a matrix A that represents the number of bushels of each crop i that are shipped to each outlet j. State what each entry aij of the matrix represents. (b) Write a matrix B that represents the profit per bushel of each fruit. State what each entry bij  of the matrix represents. (c) Find the product BA and state what each entry of the matrix represents.

Answer 1

(a)

A=$\begin{bmatrix} 125 & 100 & 75 \\ 100 & 175 & 125 \end{bmatrix}$

$a_{ij}$ represents the number of units of crop i that the grower ships to outlet j.

(b)

B=$$\begin{bmatrix} 3.50 & 6.00 \\ \end{bmatrix}$

$b_{ij}$ is the profit per unit.

(c)

BA=$$\begin{bmatrix} 3.50 & 6.00 \\ \end{bmatrix}\begin{bmatrix} 125 & 100 & 75 \\ 100 & 175 & 125 \end{bmatrix}$

BA=$$\begin{bmatrix} 1037.50 & 1400 & 1012.50 \\ \end{bmatrix}$

entries represent total profit at each outlet.