Question

The vector u = (2700, 3700) gives the number of units of two models of laptops produced by a company. The vector v = (1900, 950) 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 6%.

Answer 1

Well, what is 6% of "v"? well, 6% of anything is just 6/100 * anything, so 6% of v is just 6/100 * v or 0.06v

so, v + 0.06v is just 1.06v  <--- that'd be the increased price for <1900, 950>

well, what's that vectors wise?  < 1900 * 1.06  , 950 * 1.06 >

that is <2014 , 1007>

now.. the Revenue is just price * quantity

so, I take it, it's just asking for the dot product of <2014, 1007> • <2700, 3700>

which should just be (2014 * 2700) + (1007 * 3700)