Profit-and-loss analysis. red tide is planning a new line
of skis. for the first year, the fixed costs for setting up
production are $45,000. the variable costs for producing
each pair of skis are estimated at $80, and the selling
price will be $450 per pair. it is projected that 3000 pairs
will sell the first year.
a) find and graph c(x), the total cost of producing
x pairs of skis.
b) find and graph r(x), the total revenue from the sale
of x pairs of skis. use the same axes as in part (a).
c) using the same axes as in part (a), find and graph
p(x), the total profit from the production and sale of
x pairs of skis.
d) what profit or loss will the company realize if the
expected sale of 3000 pairs occurs?
e) how many pairs must the company sell in order to
break even?

a. -0.3 > -0.33

the value of v.w= -12.

step-by-step explanation:

we are given three vector r,v and w as:

r = < 5, -5, -2> ; v = < 2, -8, -8> ; w = < -2, 6, -5>

we know that r,v and w could also be represented as:

r=5i-5j-2k

v=2i-8j-8k

and w= -2i+6j-5k

where i,j and k are the unit vectors of x,y and z-axis respectively.

also we know that it has the following property:

i.i=1 ; j.j=1; k.k=1

and i.=j.i=i.k=k.i=j.k=k.j=0

i.e. when we multiply two vectors or we find it's dot product we need to only multiply the components of x coordinates with each other; y with each other and z with each other.

hence, v.w= (2i-8j- -2i+6j-5k)

                  = 2×(-2)+(-8)×(6)+(-8)×(-5)

                  = -4-48+40

                  = -12

hence, v.w= -12

it is b)

hope this : )

step-by-step explanation: