Biology Forums - Study Force

A meat department manager discovers that she can sell m(x) kilograms of ground beef in a week, where m(x) = 14700 - 3040x, if she sells it at x dollars per kilogram. She pays her supplier $3.21/kg for the beef.
a) Determine an algebraic expression for p(x), where p(x) represents the total profit in dollars for 1 week.

b) Find the equation for the inverse relation. Interpret its meaning.

c) Write an equation in function notation to represent the price that will earn $1900 in profit. Evaluate and explain.

d) Determine the price that will maximize profit.

e) The supply cost drops to $3.10/kg. What price should the manager set? How much profit will be earned at this price?

 :)

Thanks, but my teacher said the slader one is incorrect, so I'm not sure

Here are the solutions

Hi Emily, I'm siding this @duddy on this one. Could be your textbook is wrong, but what's concerning is your teacher disagreeing with it.

My notes

Heres the teachers solution

I see what she did differently, she substitute the function m(x) into the profit function:

Revenue function: R(x) = x*m(x)

Cost function: C(x) = 3.21*x

Profit function:

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

P(x) = x*m(x) - 3.21*x

Then she inserted m(x) = 14700 - 3040x into the bolded x, but it's not correct because x represents x dollars per kilogram. Place x into the cost function $3.21 / kg will not cancel out the units correctly.

I'll be back in 30 mins to 1 hour

Okay, I've been analyzing this for hours. I finally have come up with a conclusion, so hear me out. First and foremost, thanks for the question, I always appreciate a challenge.

We're told in the question that m(x) represents kilograms, hence why m was used to represent mass.

Profit is revenue minus cost, and both revenue and cost are $ units.

x, as per the question, has the units $/kg.

If we multiply m(x) * x we get $ unit > revenue
If we multiply c(x) * x, we won't get $ unit, so this is wrong. Duddy's answer is wrong
However, if we multiply c(x) with m(x), we get $ units.

Therefore,

P(x) = m(x) * x - c(x) * m(x)

YOUR TEACHER IS RIGHT

Content hidden

Thanks so much, it really helped me! But for the a) I tried to factor it out by using the quadratic formula and my x-intercepts were x = 3.21 and x = 4.84, but the answer from the textbook is written p(x) = (x-3.21)(14700-3040x), is that the same thing, or did I do something wrong? And for b) the textbook is shown a little differently, like ex. the square root part shows -x + 2008, but I do get that answer when doing algebra if that makes sense, so I'm guessing it's okay to write it as (24458.4)^2 - 12160(x + 47187) in the square root. And I also didn't get the 6080 underneath the square root, since it says 3040 from the textbook. Just want to make sure, Thanks

hi emily, yes, it's all the same. It's written differently because in the answer they put it in factored form -- that's not important, question doesn't ask for it.

The quadratic part is the same mathematically, don't worry about the way it looks. As you see, (c) came out the same, so that means the equations are equivalent

okay thank u!

Marking the topic solved :)

thankss

thanks

Thank you

Thanks

thank you

Thank you

Thank you so much

Post Merge: 6 months ago

Hey bio_man I just found this question in my text book. I was wondering if you could explain Part a in a simpler way for me to understand.

I explained it in this post.

So the revenue function \(R(x)\) is:

\[R(x) = x \cdot m(x) \]

The cost function \(C(x)\) is:

\[C(x) = 3.21 \cdot m(x) \]

The profit function \(P(x)\) is:

\[P(x) = R(x) - C(x)\]

Simplify this equation and then factor to get:

\[P(x) = (x-3.21)(14700 - 3040x)\]

Does that help?

yes that makes a lot more sense now thank you

Thank you so much

Thanks!

Thx

Thank you so much

Thanks!