The vector $\mathbf { u } = \langle 3700,4600 \rangle$ gives the number of units of two models of laptops produced by a company. The vector $\mathbf { v } = \langle 1550,1150 \rangle$ gives the prices (in dollars) of the two models of laptops, respectively. Identify the vector operation used to increase revenue by $3 \%$.
A) $\mathbf { u } \cdot ( 1.03 ) \| \mathbf { v } \|$
B) $1.03 ( \mathbf { u } \cdot \mathbf { v } )$
C) $1.03 \| \mathbf { u } \cdot \mathbf { v } \|$
D) $1.03 \| \mathbf { u } \| \cdot \mathbf { v }$
E) $1.03 ( \mathbf { u } + \mathbf { v } )$

Question

Quizplus · Accepted Answer

To increase revenue by 3%, we need to multiply the original revenue by 1.03. Revenue is given by the dot product of the unit and price vectors, so to increase revenue by 3%, we can multiply the dot product by 1.03. Therefore, the correct expression is $1.03 (\mathbf{u} \cdot \mathbf{v})$.

The Vector u=⟨3700,4600⟩\mathbf { u } = \langle 3700,4600 \rangleu=⟨3700,4600⟩ Gives the Number of Units of Two Models of Laptops

The Vector $\mathbf { u } = \langle 3700,4600 \rangle$ Gives the Number of Units of Two Models of Laptops