A fruit grower raises two crops apples and peaches Each of t

A fruit grower raises two crops, apples and peaches. Each of these crops is shipped to three different outlets. The number of units of crop i that are shipped to outlet j is represented by a_ij in the matrix.

A =

The profit per unit is represented by the matrix

B =

Find the product BA.

BA =

State what each entry of the product represents.

A.)The entries represent the profits from both crops at each of the three outlets.

B.) The entries represent the total number of crops at each of the three outlets.     

C.) The entries represent the profits made for each individual crop.

D.) The entries represent the cost to produce each crop at the three outlets.

E.) The entries represent the total amount that is shipped to each of the three outlets.

	105	115	80
85	170	105

Solution

The product BA ( of a 1x2 matrix and a 2x3 matrix) isa 1x3 matrix as under:

$992.50

$1510

$977.50

The entries in the 1^st row of A represents the number of units of apples shipped to 3 different outlets and the entries in the 2nd row of A represents the number of units of peaches shipped to the same 3 outlets. The entries in the matrix B mean that the profit per unit of apples is $ 5 and the profit per unit of peaches is $ 5.50. The entry of $ 992.50 represents profit to the farmer from sale ( of both apples and peaches) to the 1^st of the 3 outlets. The entry of $ 1050 represents profit to the farmer from sale ( of both apples and peaches) to the 2nd of the 3 outlets and the entry of $ 977.50 represents profit to the farmer from sale ( of both apples and peaches) to the 3rd of the 3 outlets.

The entries represent the profits from both crops at each of the three outlets. Option A is the correct answer.