The vector u = (4300, 5200) gives the number of units of two models of laptops produced by a company. The vector v = 1800, 1200 gives the prices (in dollars) of the
two models of laptops, respectively. Identify the vector operation used to increase revenue by 5%.
(the // represent the straight brackets that are used, not division symbols)
A. u⋅(1.05) //v//
B. 1.05(u ⋅ v)
C. 1.05(u + v)
D. 1.05// u⋅v//
E. 1.05 // u // ⋅v
u dot v = revenue
which is sum of number of each times price of each
so
1.05 ( u dot v )
To increase revenue by 5%, we need to multiply the vector representing prices (v) by 1.05. Therefore, the correct vector operation is:
E. 1.05 // u // ⋅v
To increase revenue by 5%, we need to multiply the revenue vector by 1.05. The revenue vector can be obtained by multiplying the number of units vector (u) by the prices vector (v).
So, the correct option would be C. 1.05(u + v).
To calculate it using the given values, you would perform the following steps:
1. Multiply the number of units vector (u) by the prices vector (v): u ⋅ v = (4300 * 1800) + (5200 * 1200) = 7740000 + 6240000 = 13920000.
2. Add the number of units vector (u) and the prices vector (v): u + v = (4300 + 1800, 5200 + 1200) = (6100, 6400).
3. Multiply the sum vector by 1.05 to increase the revenue: 1.05(u + v) = 1.05(6100, 6400) = (6405, 6720).
So, the vector operation used to increase revenue by 5% is 1.05(u + v), which corresponds to option C.