Question 963939


{{{P= -2b^2 + 14b -20}}}

set {{{P=0}}} and find {{{b}}}

{{{0= -2b^2 + 14b -20}}}..........factor out {{{-2}}}

{{{0= -2(b^2 -7b +10)}}}....factor {{{-1}}} out

{{{0= -2(b^2 - 7b +10)}}}......write {{{-7b}}} as {{{-2b-5b}}}

{{{0= -2(b^2 - 2b-5b +10)}}}...group

{{{0= -2((b^2 - 2b)-(5b -10))}}}

{{{0= -2(b(b - 2)-5(b -2))}}}

{{{0= -2((b-5)(b -2))}}}

solutions:

{{{b=5}}} and {{{b=2}}}=> since in thousands, company need to produce {{{5000}}} or {{{2000}}} skateboards to break even

 maximum profit occurs at {{{b=(5+2)/2=7/2=3.5}}}=> in thousands {{{3500}}}

so, foe Wheely Fast need to produce {{{3500)skateboards to maximize profit

what will be the maximum profit:

{{{P= -2((b-5)(b -2))}}}............substitute {{{b=3.5}}}

{{{P= -2((3.5-5)(3.5 -2))}}}
{{{P= -2(-1.5)(1.5)}}}
{{{P= -2(-1.5)(1.5)}}}
{{{P= -2(-2.25)}}}
{{{P= 4.5}}}=> in hundred thousands of dollars will be {{{P= 450000}}}