The vector $\mathbf { u } = \langle 3900,4000 \rangle$ gives the number of units of two models of laptops produced by a company.The vector $\mathbf { u } = \langle 1450,1000 \rangle$ gives the prices (in dollars) of the two models of laptops, respectively.Identify the vector operation used to increase revenue by 6%.
A) 1.06(u + v)
B)1.06 $\left\| \mathbf { u } ^ { \prime } \mathbf { v } \right\|$
C) $\mathbf { u } \cdot ( 1.06 ) \| \mathbf { v } \|$
D)1.06 $\left( \mathbf { u } ^ { * } \mathbf { v } \right)$
E)1.06 $\| \mathbf { u } \| ^ { . } \mathbf { v }$

Question

Quizplus · Accepted Answer

To increase revenue by 6%, you multiply the dot product of the quantity vector $\mathbf{u}$ and the price vector $\mathbf{v}$ by 1.06. The dot product gives the total revenue, and multiplying by 1.06 increases it by 6%. The notation $\mathbf{u}^{*}\mathbf{v}$ is not standard for dot product, but in this context, it suggests the operation of combining the two vectors element-wise (which is what the dot product does) and then scaling the result, which aligns with increasing revenue by 6%.

The Vector u=⟨3900,4000⟩\mathbf { u } = \langle 3900,4000 \rangleu=⟨3900,4000⟩ Gives the Number of Units of Two Models of Laptops

The Vector $\mathbf { u } = \langle 3900,4000 \rangle$ Gives the Number of Units of Two Models of Laptops