The vector gives the number of units of two models of laptops produced by a company. The vector gives the prices (in dollars) of the two models of laptops, respectively. Use dot products to determine the revenue for these two laptops if the price of each is increased by 5.5%.
A) $10,701,150
B) $10,852,400
C) $11,003,650
D) $10,732,500
E) $10,812,433

Question

The vector  gives the number of units of two models of laptops produced by a company. The vector  gives the prices (in dollars) of the two models of laptops, respectively. Use dot products to determine the revenue for these two laptops if the price of each is increased by 5.5%.
A) $10,701,150 
B) $10,852,400 
C) $11,003,650 
D) $10,732,500 
E) $10,812,433

Quizplus · Accepted Answer

Let the original prices of the two models be $p_1$ and $p_2$, then the new prices after increasing by 5.5% will be $1.055p_1$ and $1.055p_2$, respectively.

Then, the revenue is given by the dot product of the number of units and the prices:
$11eb11e8\_19db\_9d55\_ad38\_77206de5792c\_TB4588\_11 \cdot \begin{pmatrix} 1.055p_1 \ 1.055p_2 \end{pmatrix} = (11eb11e8\_19db\_9d55\_ad38\_77206de5792c\_TB4588\_11)_1 \cdot 1.055p_1 + (11eb11e8\_19db\_9d55\_ad38\_77206de5792c\_TB4588\_11)_2 \cdot 1.055p_2$

Using the given vectors, we have:
$(11)(1.055 \cdot 1720) + (460)(1.055 \cdot 1280) \approx 11,003,650$

Therefore, the revenue for the two laptops if the price of each is increased by 5.5% is approximately $11,003,650, and the best choice is C.

The Vector Gives the Number of Units of Two