4. We run several local businesses that are in need of restocking items for sale
ID: 3135978 • Letter: 4
Question
4. We run several local businesses that are in need of restocking items for sale. Each store has three different warehouses that they can order from, each with its own price for each of the items. The needs of each store and the prices are as follows: Store Item1 Item2 Item3 Item4 00 80 90 70 40 30 30 80 50 50 50 Item Warehousel Warehouse2 Warehouse3 $1.00 $1.50 $2.00 $1.70 $1.20 $1.80 $1.20 $1.40 $1.50 $1.20 $1.40 $1.90 (a) Let A be the matrix representing the store needs and B be the matrix describing item costs. Explain what each term in the matrix AB repre- sents. o) Whieh wareboue teudeach of te store rder fomn? (Hine: Flad AB to help answer this question.)Explanation / Answer
There appears to be a misprint. The question will make sense only if the entries in the 1st column in matrix B read as Item 1, Item 2, Item 3, Item 4 instead of Itema, Item B, ItemC, Item D. With this presumption, we have A =
100
80
30
50
50
90
30
50
70
40
80
50
and B =
$1.00
$1.20
$1.50
$1.50
$1.80
$1.20
$2.00
$1.20
$1.40
$1.70
$1.40
$1.90
Then AB =
$365
$370
$383
$330
$328
$320
$375
$322
$360
(a). Let aij denote the ijth entry in the matrix AB. Then aij denotes the cost of all the items (1,2,3 and 4) purchased by the ith store (1 i3, A = 1,B =2, C = 3) from the jth warehouse(1 j 3). For example, a11 = $ 365 represents the cost of all the items in store A, if purchased from the 1st warehouse. Similarly, a23 = $ 320 represents the cost of all the items in store B, if purchased from the 3rd warehouse.
(b). Each sore (A,B,C) should logically purchase the items from from a warehouse, where the price of all these items (1,2,3,4) is least. Thus, store A should purchase from the 1st warehouse, store B should purchase from the 3rd warehouse and store C should purchase from the 2nd warehouse.
100
80
30
50
50
90
30
50
70
40
80
50
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