December 31st, 2009, 11:11 AM  #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, 07:56 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, 05:15 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, 05:32 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, 05:58 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, 06:07 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, 11:56 AM  #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, 03:41 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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