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May 25, 2015

Posted by **anonymous** on Friday, February 11, 2011 at 4:32pm.

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**anonymous**, Friday, February 11, 2011 at 6:17pmcould anyone help me please?

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**Ms. Sue**, Friday, February 11, 2011 at 6:33pmThere's probably a formula for figuring this out -- but I don't know it. A math tutor may be on later who can help.

I've been working with trial and error -- and I'm up to 9 weeks when she'd get $94.50 for a 135-pound hog. You can keep working with trial and error.

Your problem doesn't state what her costs are for feeding these hogs until she can reach the maximum price.

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**Anonymous**, Friday, February 11, 2011 at 7:52pmthe answers got to be 13wks and $96. but i couldn't get it.

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**Ms. Sue**, Friday, February 11, 2011 at 8:12pmIf you count the original weight of 90 pounds and $0.88 as the first week, then the 13th week is 150 pounds at $0.64, then the price is $96.

By my calculations, week 14 would see a 155-pound hog at $0.62 = $96.10

The question is terribly flawed because it doesn't take into consideration the costs of feeding the hogs.

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**tchrwill**, Saturday, February 12, 2011 at 6:44pmHow many weeks should Ms. Linton wait before taking her hogs to market in order to receive as much money as possible?

As the weight increases, the price decreases, the maximum income to be derived when the product of the weight and price is maximum.

We know that the weight W = 90 + 5w and the price P = 88 - 2w, w being the number of weeks to maximum income.

W = 90 + 5w

P = 88 - 2w

W(P) = (90 + 5w)(88 - 2w) yielding

w^2 - 26w - 792

Eq

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**tchrwill**, Saturday, February 12, 2011 at 6:58pmSorry - I hit the send key by mistake.

How many weeks should Ms. Linton wait before taking her hogs to market in order to receive as much money as possible?

As the weight increases, the price decreases, the maximum income to be derived when the product of the weight and price is maximum.

We know that the weight W = 90 + 5w and the price P = 88 - 2w, w being the number of weeks to maximum income.

W = 90 + 5w

P = 88 - 2w

W(P) = (90 + 5w)(88 - 2w) yielding

w^2 - 26w - 792

Equating to zero and taking the first derivitive yields 2w - 26 = 0 making w = 13 weeks.

At the start of week #1, the weight = 90 lbs. and the price = 88 cents per pound. At the end of week 13, the weight is 90 + 5(13) = 155 lbs. and the price is 88 - 2(13) = 62 cents per pound.

Thus, during the 14th week, the hogs are sold on the basis of a weight of 155 lbs. and a selling price of 155(.62) = $96.10 each.