farmer Linton wants to find the best time to take her hogs to market. The current price is 88cents per pound, and her hogs weigh an average of 90 pounds. the hogs gain 5 pounds per week, and the market price for hogs is falling each week by 2 cents per pound. How many weeks should Ms. Linton wait before taking her hogs to market in order to receive as much money as possible? at the time, how much money (per hog) will she get?
could anyone help me please?
There'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.
the answers got to be 13wks and $96. but i couldn't get it.
If 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.
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
Eq
Sorry - 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.
To find the best time for Farmer Linton to take her hogs to market, we need to determine when the price will be highest. Let's break down the problem step by step:
1. First, let's find out how many weeks it will take for the market price to reach the lowest point. The hogs' weight gain per week is constant at 5 pounds, and the market price falls by 2 cents per pound each week. To find when the market price will reach its lowest, we can divide the weight gained per week by the decrease in price per pound: 5 pounds / 0.02 dollars (2 cents) = 250 weeks.
2. Now that we know it will take 250 weeks for the market price to reach the lowest point, we need to calculate how many pounds the hogs will weigh at that time. The hogs currently weigh 90 pounds, and they gain 5 pounds per week, so after 250 weeks, they will weigh: 90 pounds + (5 pounds/week x 250 weeks) = 1240 pounds.
3. Next, let's determine the market price at the lowest point. The market price currently stands at 88 cents per pound and decreases by 2 cents per pound each week. So, at the lowest point in 250 weeks, the market price will be: 88 cents - (0.02 dollars/week x 250 weeks) = 88 - 5 = 83 cents per pound.
4. Now, we need to find out how many weeks after the lowest point it will take for Farmer Linton to maximize her profit. After the market price hits its lowest, waiting longer would cause the weight gain to surpass the price decrease, resulting in a decrease in profit. Hence, she should aim to sell the hogs immediately after the market price hits the lowest point.
5. Finally, to calculate the total money per hog, we multiply the weight of the hogs at the lowest point (1240 pounds) by the market price per pound (83 cents): 1240 pounds x $0.83 = $1,027.20.
So, the best time for Farmer Linton to take her hogs to market is after 250 weeks. At that time, she will receive $1,027.20 per hog.