AGRICULTURE A fruit grower raises two crops, apples and...

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 $a_{ij}$ of the matrix represents. (b) Write a matrix $B$ that represents the profit per bushel of each fruit. State what each entry $b_{ij}$ of the matrix represents. (c) Find the product $BA$ and state what each entry of the matrix represents.

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 $a_{ij}$ of the matrix represents.
(b) Write a matrix $B$ that represents the profit per bushel of each fruit. State what each entry $b_{ij}$ of the matrix represents.
(c) Find the product $BA$ and state what each entry of the matrix represents.

Transcript

00:01 Now over here in this question we've been given that there are two crops that are being grown.

00:07 What are those two of apples and peaches? okay so apples and peaches are being grown in a farm and they are being sold in three different outlets.

00:20 So we've been given the information regarding the number of bushels of apples that are sent to the three outlets as well as the number of peaches.

00:27 Also we've been provided the information of the profit that is made per bushel for apples and peaches.

00:34 Now, the first part, the motion is just asking you to frame a matrix 8 that represents the number of bushels for each crop that is being shaped to each of the outlets.

00:46 Right.

00:46 So, as i say, there are two crop over here and there are three outlets.

00:52 So, this will be a two by three ordered matrix.

00:56 Right.

00:56 The rows will represent the crops you can see and the three columns will represent the three different outlets so the apples that are being sold at the three different outlets are 125 and 75 and 75 and the number of bushels of peaches that are being sold at the three different outlets are 100 175 and 125 so this is the required matrix and the entries over here just represent the number of bushels of each crop that are shaped to three different outlets.

01:30 This is outlet one, you say outlet two and three.

01:34 I mean the columns are representing the outlets whereas the rows are representing the crops.

01:39 But coming on to the b part, now we are supposed to frame a matrix and represents a crofted per bushel of each fruit.

01:47 So as i said, we've been already given the information of the profit that is made from each crop.

01:54 So from i mean in the question itself it is already stated and the profit per bushel for apples is 3 .5 dollars whereas the profit per portion for peaches is $6.

02:07 So simply it will be just a row matrix 3 .50 will be one element and the other element will be 6 .00.

02:16 This is just the row matrix now and what are the entries of this matrix representing simply the entries represent the profit.

02:24 Per bushel of each crop...

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