You are Here: Home

# Working out maximum total revenue watch

1. I had the following question on an exam paper and I've been stuck on it for more than an hour and it's driving me crazy. I've used Google and YouTube but I'm still no closer to working it out. Could anyone help me out? I'd appreciated it! Thank you.

Assume the total revenue function for a specific product is given by TR = –X2 + 6X + 1, where X is the quantity of the product in question. What is the maximum total revenue that can be obtained (TRMAX) and at what level of output will this be achieved (X*)?

• a) TRMAX = 28, X* = 3
• b) TRMAX = 3, X* = 10
• c) TRMAX = 10, X* = 3
• d) None of the above
2. (Original post by ImNotSuperman)
I had the following question on an exam paper and I've been stuck on it for more than an hour and it's driving me crazy. I've used Google and YouTube but I'm still no closer to working it out. Could anyone help me out? I'd appreciated it! Thank you.

Assume the total revenue function for a specific product is given by TR = –X2 + 6X + 1, where X is the quantity of the product in question. What is the maximum total revenue that can be obtained (TRMAX) and at what level of output will this be achieved (X*)?

• a) TRMAX = 28, X* = 3
• b) TRMAX = 3, X* = 10
• c) TRMAX = 10, X* = 3
• d) None of the above
What is the condition for Total Revenue to be maximised? How can you find that using the Total Revenue function? Once you know that it's trivial to work out.
3. (Original post by The Financier)
What is the condition for Total Revenue to be maximised? How can you find that using the Total Revenue function? Once you know that it's trivial to work out.
I have no idea
4. (Original post by ImNotSuperman)
I had the following question on an exam paper and I've been stuck on it for more than an hour and it's driving me crazy. I've used Google and YouTube but I'm still no closer to working it out. Could anyone help me out? I'd appreciated it! Thank you.

Assume the total revenue function for a specific product is given by TR = –X2 + 6X + 1, where X is the quantity of the product in question. What is the maximum total revenue that can be obtained (TRMAX) and at what level of output will this be achieved (X*)?

• a) TRMAX = 28, X* = 3
• b) TRMAX = 3, X* = 10
• c) TRMAX = 10, X* = 3
• d) None of the above
You need to differentiate the TR formula. If you differentiate it you get dTR/dx = -2x + 6. In order to find the stationary point of a graph (i.e. the maximum and/or minimum) you need to make the differential equal to 0. This gives us -2x + 6 = 0, which gives us that x = 3. If you sub x = 3 back into the initial TR formula, you get TR = 10. Based on that logic, I believe the answer would be c. I am not 100% sure if what I have done is correct, but assuming it is, feel free to ask me for more of an explanation behind my logic.
5. (Original post by ImNotSuperman)
I have no idea
Hint: If total revenue is maximised, you want the point where you can't increase revenue any further. What measures the additional revenue gained from selling a unit? M........
6. (Original post by KevinLonge)
You need to differentiate the TR formula. If you differentiate it you get dTR/dx = -2x + 6. In order to find the stationary point of a graph (i.e. the maximum and/or minimum) you need to make the differential equal to 0. This gives us -2x + 6 = 0, which gives us that x = 3. If you sub x = 3 back into the initial TR formula, you get TR = 10. Based on that logic, I believe the answer would be c. I am not 100% sure if what I have done is correct, but assuming it is, feel free to ask me for more of an explanation behind my logic.
I appreciate what you're doing here but at an undergraduate level, they need to get to this by themselves otherwise they're not really understanding and grasping the concept to the same degree. In future, if a post is marked undergraduate, could you not post the full solution? Just like the maths forum, I'd prefer nudges in the right direction.
7. (Original post by The Financier)
I appreciate what you're doing here but at an undergraduate level, they need to get to this by themselves otherwise they're not really understanding and grasping the concept to the same degree. In future, if a post is marked undergraduate, could you not post the full solution? Just like the maths forum, I'd prefer nudges in the right direction.
Yeah, perfectly acceptable. I was in a hurry so I basically just dropped off the answer and planned to leave haha, but I completely see what you mean. I will bear this in mind for future responses.
8. Thanks to both of you - I really appreciate it. I didn't realise it was as simple as that!

TSR Support Team

We have a brilliant team of more than 60 Support Team members looking after discussions on The Student Room, helping to make it a fun, safe and useful place to hang out.

This forum is supported by:
Updated: November 7, 2016
Today on TSR

### ULTIMATE packing list for uni

Poll
Useful resources

The Student Room, Get Revising and Marked by Teachers are trading names of The Student Room Group Ltd.

Register Number: 04666380 (England and Wales), VAT No. 806 8067 22 Registered Office: International House, Queens Road, Brighton, BN1 3XE