Question

Complete these activities. Consider the following information from Tiger Oil Company: By multiplying matrices, calculate the matrix for total dollar volume of sales.

Answer 1

Answer:

28,000

10,500

3,700

Step-by-step explanation:

Regular                  Premium

No.1      20                   30

No.2      15                    5

No.3       5                     2

regular cost per gallon - 500

premium cost per gallon - 600

first, you multiply 20 & 500= 10,000 then, you multiply 30 & 600= 18,000.

next, you add them 10,000+18,000=28,000

and you repeat filling in the other numbers.

15*500 = 7,500      5*600 = 3,000       7,500 + 3,000 = 10,500

5*500 = 2,500        2*600 = 1,200        2,500 + 1,200 = 3,700

Answer 2

Given the matrix

$\left[\begin{array}{cc}20&30\\15&5\\5&2\end{array}\right]$

representing the number of thousands of gallons of regular and premium oil sold by the three stations of Tiger oil company and the matrix

$\left[\begin{array}{c}500\\600\end{array}\right]$

representing dolloars per thousands of gallons of regular and premium oil sold by Tiger oil company.

The matrix for total dollar volume of sales using matrix multiplication is given by:

$\left[\begin{array}{cc}20&30\\15&5\\5&2\end{array}\right] \left[\begin{array}{c}500\\600\end{array}\right]= \left[\begin{array}{c}20(500)+30(600)\\15(500)+5(600)\\5(500)+2(600)\end{array}\right] \\ \\ = \left[\begin{array}{c}10000+18000\\7500+3000\\2500+1200\end{array}\right] =\left[\begin{array}{c}28000\\10500\\3700\end{array}\right]$

Therefore, the total dolar volume of sales is per thousand of gallons of oil is given by:

$\left[\begin{array}{c}28000\\10500\\3700\end{array}\right]$