My Math Forum Maximizing Profits Problem

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 December 31st, 2009, 12:11 PM #1 Newbie   Joined: Dec 2009 Posts: 4 Thanks: 0 Maximizing Profits Problem Looking for some guidance for this problem, I will add information as I go along. I think the steps are: 1) Develop a formula that represents the cost 2) Find critical points 3) evaluate the critical points What I am unsure of is am I allowed to vary the length of the highway and gravel road? I'm asked to maximize profit or I can minimize cost. Is this cost of operating or of construction as well? If it's of operating only, I can easily deduct the construction cost from the inital 7.8 million. Also if it's of operating only, can I not say operate as fast as possible to reduce hours? Please advise thank you.
 December 31st, 2009, 08:56 PM #2 Senior Member   Joined: Jan 2009 From: Japan Posts: 192 Thanks: 0 Re: Maximizing Profits Problem Is this the entirety of the problem? I have exactly the same questions as you. Either there's more to this problem than what's posted or it's a badly constructed problem.
 January 2nd, 2010, 06:15 AM #3 Newbie   Joined: Dec 2009 Posts: 4 Thanks: 0 Re: Maximizing Profits Problem Hi, This is the entire problem. I have nothing more. Im confused on the location of the road, if im allowed to move the gravel road or not.
 January 2nd, 2010, 06:32 AM #4 Senior Member   Joined: Jan 2009 From: Japan Posts: 192 Thanks: 0 Re: Maximizing Profits Problem I would assume, then, that you're allowed to build wherever you like, if you're not permitted to ask the person who assigned this question. I would not assign such a problem, but if I did by mistake, you'd get full credit for making the assumption (and stating that you are) and then solving the problem.
 January 2nd, 2010, 06:58 AM #5 Newbie   Joined: Dec 2009 Posts: 4 Thanks: 0 Re: Maximizing Profits Problem Thank you for your reply, i think i will do each of these methods since i cant find which one is correct :
 January 2nd, 2010, 07:07 AM #6 Senior Member   Joined: Jan 2009 From: Japan Posts: 192 Thanks: 0 Re: Maximizing Profits Problem I would skip 2 -- it's what's called a "completely dominated" strategy. Case 1 is better than any of case 2 since the highway is cheaper both to pave and to travel on.
 January 3rd, 2010, 12:56 PM #7 Newbie   Joined: Dec 2009 Posts: 4 Thanks: 0 Re: Maximizing Profits Problem I used number 3, if you look at 1 and 3 closely you will notice that after minimizing 3, 1 is a possibility. Although, after solving the problem 1 is not the answer.
 January 3rd, 2010, 04:41 PM #8 Senior Member   Joined: Jan 2009 From: Japan Posts: 192 Thanks: 0 Re: Maximizing Profits Problem Yes. I would personally "solve" for 1 just because the instructions are ambiguous at best, not because the technique used to optimize 3 would not find 1 if it were the best answer.

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