Question

The total cost of producing x items per day is x^2/3 + 45x + 27 dollars, and the price per
item at which each may be sold is 60− 12x dollars. Find an expression for the daily profit.

Answer 1

@oldrin.bataku help please

Answer 2

So I can't help?

Answer 3

lol @wio nice one.

Answer 4

umm anyone help please?

Answer 5

You need to find the total revenue

Answer 6

You have the revenue per item:\[ 60− 12x\]

Answer 7

Multiply this by the number of items to get the revenue.

Answer 8

@AonZ Does this help, or are you still lost?

Answer 9

It doesnt tell us the number of items sold?

Answer 10

btw this is part 1 of the question anyways

Answer 11

What do you think \(x\) is?

Answer 12

Firstly we should keep in mind that Profit is the difference between revenue and cost and shown like this:\[\bf P(x)=R(x)-C(x)\]Where 'P' is profit, 'R' is revenue, 'C' is cost.
We are already given the cost function so we just need the revenue function..

We know that each item can be sold for \(\bf 60 -12x\) dollars hence the total revenue is given by the number of items multiplied by the selling price which gives us our revenue function as:\[\bf R(x)=x(60-12x)=60x-12x^2\]Now plug in C(x) to get P(x). Hence:\[\bf P(x)=R(x)-C(x)=60x-12x^2-\left( \frac{ 1 }{ 3 } x^2+45x+27)\right)\]\[\bf = 15x-\frac{ 37 }{ 3 }x^2-27\]

Answer 13

@AonZ

Answer 14

Well...

Answer 15

hmm answer in the back of my book doesnt match up with it :/

Answer 16

instead it has -5/6 x^2 + 15x - 27

Answer 17

nvm sorry you got it right

Answer 18

maybe i made a computational mistake which i don't think i made but we can always double check

Answer 19

=.=...

Answer 20

thanks to both of you

Answer 21

@AonZ I hope you understood it