Chapter 6.4, Problem 71E

(a)

To determine

To Find: The dot product $u\cdot v$ and interpret the result in the context of the problem.

Answer to Problem 71E

The value of $u\cdot v=89201.5$product shows that the total cost of the cellular phones is produced by the company.

Explanation of Solution

Given:

The vector $u=\langle 1225,2445\rangle$ and vector $v=\langle 12.20,8.50\rangle$ .

Calculation:

The vector product $u\cdot v$ is obtained as,

  $\begin{array}{c}u\cdot v=\langle u_1,u_2\rangle \cdot \langle v_1,v_2\rangle \\ =\langle 4600,5250\rangle \cdot \langle 79.99,99.99\rangle \\ =4600\left(79.99\right)+5250\left(99.99\right)\\ =89201.5\end{array}$

The product shows that the total cost of the cellular phones is produced by the company.

(b)

To determine

To Find: The vector operation used to increase wages by $2\%$ .

Answer to Problem 71E

The price is increased by $2\%$ , the vector operation called scalar multiplication is used.

Explanation of Solution

Consider the formula for the scalar multiplication is,

  $\begin{array}{c}c\left(u\cdot v\right)=cu\cdot v\\ =u\cdot cv\end{array}$

Thus, to increase the price by $5\%$ use the vector operation called the scalar multiplication. This gives the total new cost of the cellular phones produced by the company as,

  $u\cdot \left(1.02\right)v=1.02\left(u\cdot v\right)$

Thus, to increase the price by $2\%$ use the vector operation called scalar multiplication.