WatkinsonMolly
New member
- Joined
- Oct 24, 2011
- Messages
- 6
Hi guys, this homework is driving me up the wall. The question is as follows:
A producer can sell x instruments per week for m dollars each, where m=500 - (x/24). His cost of producing x instruments is 125x + 5000 dollars. Find the amount of instruments that should be produced in a week to obtain maximum profit.
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So what I did first was take the integral of m, because m gives the profit you make on that particular amount of instrument, so the integral should equal the total revenue (not profit), which I calculated to r=500x - (x^2 /48) + a constant C. Then, I saw that when x=1, m=r, so I substituted them to solve for the constant C. 500 - 1/24 = 500 - 1/48 + C, and got C= -1/48, so r = 500x - (x^2)/48 -1/48.
Then I evaluated Profit (P) as being Revenue - Cost, P= R-C. Then, to calculate the maximum profit, I had to calculate P', which I got to = 375 - (2x / 48). When P' = 0, the profit will be maximized, so I set it = 0. 0 = 375 - (x/24).
---> -375 = -x/24
---> 9000 = x.
This answer indicated that the profit would be maximized when the instruments produced per week is 9000. Did I do this correctly, or am I just way off? To be honest, I think I'm completely wrong, but I don't see why. Can anyone explain to me what I've done wrong? Thanks in advance!
A producer can sell x instruments per week for m dollars each, where m=500 - (x/24). His cost of producing x instruments is 125x + 5000 dollars. Find the amount of instruments that should be produced in a week to obtain maximum profit.
______________________________________________
So what I did first was take the integral of m, because m gives the profit you make on that particular amount of instrument, so the integral should equal the total revenue (not profit), which I calculated to r=500x - (x^2 /48) + a constant C. Then, I saw that when x=1, m=r, so I substituted them to solve for the constant C. 500 - 1/24 = 500 - 1/48 + C, and got C= -1/48, so r = 500x - (x^2)/48 -1/48.
Then I evaluated Profit (P) as being Revenue - Cost, P= R-C. Then, to calculate the maximum profit, I had to calculate P', which I got to = 375 - (2x / 48). When P' = 0, the profit will be maximized, so I set it = 0. 0 = 375 - (x/24).
---> -375 = -x/24
---> 9000 = x.
This answer indicated that the profit would be maximized when the instruments produced per week is 9000. Did I do this correctly, or am I just way off? To be honest, I think I'm completely wrong, but I don't see why. Can anyone explain to me what I've done wrong? Thanks in advance!