Turn on thread page Beta
    • Thread Starter
    Offline

    14
    ReputationRep:
    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
    • TSR Support Team
    • Clearing and Applications Advisor
    Offline

    21
    ReputationRep:
    TSR Support Team
    Clearing and Applications Advisor
    (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.
    • Thread Starter
    Offline

    14
    ReputationRep:
    (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
    Offline

    7
    ReputationRep:
    (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.
    • TSR Support Team
    • Clearing and Applications Advisor
    Offline

    21
    ReputationRep:
    TSR Support Team
    Clearing and Applications Advisor
    (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........
    • TSR Support Team
    • Clearing and Applications Advisor
    Offline

    21
    ReputationRep:
    TSR Support Team
    Clearing and Applications Advisor
    (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.
    Offline

    7
    ReputationRep:
    (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.
    • Thread Starter
    Offline

    14
    ReputationRep:
    Thanks to both of you - I really appreciate it. I didn't realise it was as simple as that!
 
 
 
Poll
A-level students - how do you feel about your results?

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

Write a reply...
Reply
Hide
Reputation gems: You get these gems as you gain rep from other members for making good contributions and giving helpful advice.