Homework Help

The monthly cost of producing x bows is C(x)=8+2x. The revenue produced by selling x...

user profile pic

rosey-girl | Student, Grade 12 | (Level 1) Valedictorian

Posted April 2, 2013 at 2:13 AM via web

dislike 0 like

The monthly cost of producing x bows is C(x)=8+2x. The revenue produced by selling x bows is R(X)=6x-0.3x^2. What is the number of bows you need to make and sell per month to make a profit?

1 Answer | Add Yours

user profile pic

pramodpandey | College Teacher | (Level 3) Valedictorian

Posted April 2, 2013 at 8:00 AM (Answer #2)

dislike 1 like

C(x)=8+2x. The revenue produced by selling x bows is R(X)=6x-0.3x^2.

P(x)=R(x)-C(x)

`P(x)=6x-.3x^2-8-2x`

`P(x)=-.3x^2+4x-8`

`P(x)=-(3/10)(x^2-(40/3)x+80/3)`

`=(-3/10)((x-20/3)^2-160/9)`

`=16/3-(3/10)(x-20/3)^2`

`16/3>(3/10)(x-20/3)^2`

`160/9>(x-20/3)^2`

Taking square root

`sqrt(160/9)>x-20/3`

`sqrt(160/9)+20/3>x`

`(12.65+20)/3>x`

`10.88>x`

`x<10.88`

If x=11 then P(x)=-0.3 which is loss .

If x=10 ,then P(x)=2 which is profit.

So I conclude x may be less than or equal to 10.

Join to answer this question

Join a community of thousands of dedicated teachers and students.

Join eNotes