There are three convenience stores in Folsom. This week,...

There are three convenience stores in Folsom. This week, store I sold 88 loaves of bread, 48 qt of milk, 16 jars of peanut butter, and 112 lb of cold cuts. Store II sold 105 loaves of bread, 72 qt of milk, 21 jars of peanut butter, and 147 lb of cold cuts. Store III sold 60 loaves of bread, 40 qt of milk, no peanut butter, and 50 lb of cold cuts. a. Use a $4 \times 3$ matrix to express the sales information for the three stores. b. During the following week, sales on these products at store I increased by 25$\%$ ; sales at store II increased by $1 / 3 ;$ and sales at store III increased by 10$\% .$ Write the sales matrix for that week. c. Write a matrix that represents total sales over the two-week period.

Transcript

0:00 Hello everyone.

00:01 So in this question we have given store 1 sold, 88 loaves of bread, 48 quintal of milk, 16 jars of peanut butter and 112 pounds of cold cuts.

00:12 Then store 2 soles, 105 loaves of bread, 72 quintal of milk, 21 jars of peanut butter, and 147 pounds of cold cuts.

00:23 Then store 3 souls, 60 loaves of bread, 40 quintal of milk, no peanut butter.

00:30 And 147 pounds of cold cuts.

00:30 Head butter and 50 pounds of cold cut.

00:32 Now we have to express the sales of information for these three stores using 4 cross 3 matrix.

00:40 Then we have to find the sales matrix if sales on the product at store 1, store 2 and store 3 increased by 25 % 1 divided by 3 and 10 % respectively.

00:53 And then we have to find the matrix that represents total sales over the 2 week period.

01:00 So now first of all we will express the sales information in 4 cross 3 matrix.

01:06 Now from the given information number of stores is equal to 3 and number of items is equal to 4.

01:21 So now what we will do? so now as we have to form 4 cross 3 matrix so we will write items in row 1.

01:31 And stores in column wise and there are store 1, store 2 and store 3.

01:40 And items are loaves of bread, loaves of bread, then milk, then peanut butter, peanut butter and cold cuts.

01:59 Now store 1 solds, 88 loaves of bread, store 2, 3.

02:03 Soles, 105 loaves of bread and store 3 sold 60 loaves of bread.

02:10 Then store one sole 48 quintal of milk, store 2 souls 72 quintal of milk and store 3 souls 40 quintal of milk.

02:21 Then store 1 souls 16 jars of peanut butter, store 2 souls 21 jars of peanut butter, 0 jar of peanut butter.

02:31 Now store 1 soles, 112 pounds of cold cuts, then store 2 souls 147 pounds of cold cuts and store 3 sold 50 pounds of cold cuts.

02:46 So now we got 4 cross 3 matrix.

02:52 So therefore the 4 cross 3 matrix, the 4 cross 3 matrix, the 4 cross 3 matrix, the 4 cross 3 matrix, is 88, 105, 60, 48, 78, 72, 40, 16, 2100 and 111, 147, 50.

03:19 Now we will answer the second part of the question, which says sales increased at store 1, store 1 by 25 % then at store 2, store 2 by 1 third, and at store 3, store 3 by 10%.

03:52 So now, first of all, let us consider matrix a, which is equal to 88, 105, 60, then 48, 78, 702, 40, 40, 40, then 70, 40, 40, then 70, 40, then 70, 40, 16, 210 and 112, 147 and 50.

04:15 So this is our matrix a.

04:17 Now we have to form matrix b using these informations.

04:22 And in order to find that, we have to apply some operations on column 1, column 2 and column 3.

04:30 Now column 1 represents store 1, column 2 and column 3.

04:39 Now 25 % means 25 divided by 100 which is equal to 1 divided by 4 and 10 % means 10 divided by 100 which is equal to 1 divided by 10.

04:53 So now we are transforming c1 by c1 plus 1 divided by 4 c1...

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