An auto parts store sells only three brands oftires. These are FIRESTONE, MICHEL

Question

An auto parts store sells only three brands oftires. These are FIRESTONE, MICHELLIN, and COOPER. The quarterlysales for tires in the store are as follows

25 FIRESTONE TIRES, 5 MICHELLIN TIRES, and 6COOPER TIRES sold in the first quarter.

20 FIRESTONE TIRES, 10 MICHELLIN TIRES, and 16COOPER TIRES sold in the second quarter

3 FIRESTONE TIRES, 15 MICHELLIN TIRES, and 7COOPER TIRES sold in the third quarter

2 FIRESTONE TIRES, 25 MICHELLIN TIRES, and 27COOPER TIRES sold in the fourth quarter

Find the per quarter sales of each brand of tirein the store if a FIRESTONE tire costs $33.25and a MICHELLIN tire costs $40.19and a COOPER tire costs $25.03. Your solution must beprovided as a matrix and you must use matrix multiplication tosolve the problem.

Explanation / Answer

25 FIRESTONE TIRES, 5 MICHELLIN TIRES, and 6COOPER TIRES sold in the first quarter.

20 FIRESTONE TIRES, 10 MICHELLIN TIRES, and 16COOPER TIRES sold in the second quarter

3 FIRESTONE TIRES, 15 MICHELLIN TIRES, and 7COOPER TIRES sold in the third quarter

2 FIRESTONE TIRES, 25 MICHELLIN TIRES, and 27COOPER TIRES sold in the fourth quarter

Find the per quarter sales of each???[PLEASE CHECK FOR TYPO ..IT SHOULD BE ALL BRANDS I THINK] brand of tire in the store if a FIRESTONE tirecosts $33.25 anda MICHELLIN tire costs $40.19 anda COOPER tire costs $25.03.Your solution must be provided as a matrix and you must use matrixmultiplication to solve the problem.

FRAME TWO MATRICES AS FOLLOWS

1.SALE MATRIX=S

ROWS REPRESENTING A QUARTER EACH...4ROWS

COLUMNS REPRESENTING TIRES SOLD OF ONE BRAND EACH......3 COLUMNS

SO WE GET S AS (4,3) MATRIX

2. PRICE MATRIX = P

ROWS REPRESENTING A BRAND EACH...3ROWS

COLUMN REPRESENTING UNIT PRICE OF EACHBRAND......1 COLUMNS

SO WE GET P AS (3,1) MATRIX

NOTE THAT WE MADE MATRIX COMPATABLE FORMULTIPLICATION

S(4,3)*P(3,1) = T (4,1)....TOTAL SALE VALUE INEACH QUARTER OF ALL BRANDS ..ASSUMING TYPO CORRECTION POINTEDABOVE

SO WE GET

S=




FIRESTONE MICHELIN COOPER
Q1 25 5 6
Q2 20 10 16
Q3 3 15 7
Q4 2 25 27
P=




UNIT PRICE


FIRESTONE 33.25


MICHELIN 40.19


COOPER 25.03


T= TOTAL SALEVALUE EACH QUARTER

T


Q1 1182.38


Q2 1467.38


Q3 877.81


Q4 1747.06

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