i need fast help with a math problem?

This problem has been killing me for over 2 hours now. I really need some help!
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Farmer Fay has a pig that presently wieghs 200 pounds. She could sell it now for a price of $1.40 a pound. The pig is gaining 10 pounds a week while the price per pound is dropping 2 cents a week. When should Fay sell the pig to get the maximum amount of money for it.

What I've done that has dead ended me several times now is this:
I've made a chart which provided me with the quadratic equation:
R= -2x^2-26x+280
I then found my vertex which was at (-6.5, 98)
(The x represents the numebr of weeks)

What I have gathered (however incorrectly so) from this data is that if Farmer Fay waits 6.5 she will reach maximum profits. However, this being said when I checked it on the chart...The profits made at 6.5 weeks were not $98 nor was the maximum profit made.

Help me PLEASE?! I really need some!

 

the answer is 25 weeks. 450 pounds at 90 cents/lb...

 

Thankyou....If you don't mind me asking...how did you figure it out?

 

no problem.. i just pulled a couple numbers out of the air. found where profit started to drop off, and worked backward till i found the answer. quite unremarkable, and probably not the way a math instructor would have wanted their students to do it.

 

^What he said


All I know is:
1 is for peanut butter
2 is for tuba
and 3 is for house..

 

sweet gif.. :rofl:

 

thank you soo much man.... you have no idea how much that helped

 

lol sometime i feel smart

 

Your way's much simpler though.:2thumbsup:

 

I did a unit check, and the original derived quadratic was thrown off by a digit error. in the price factor you put in a -.2x for the two-cent-a-week decrease? shoulda been -.02x. the correct quadratic is as follows:
-2x^2 + 10x + 280.
the actual maximum of the function is at x=2.5... a 225 pound pig at 90 cents a pound

 

looks like you made a mistake somewhere. first of all 10 does not go into 225 evenly. its supposed to be a 450 pound pig. 225 is half of 450 pounds.

 

the function represents a parabola that opens down. thus, the maximum should be the point where the slope is zero. so, we just take a derivative and set it to zero, and see what x is.
the derivative of the function -2x^2 + 10x + 280 is the function -4x + 10.
-4x + 10=0, x=2.5
and yes, 10 doesn't go into 225 evenly, but it is 200 +(10*2.5)

 

It should be a 450lb pig @90cents per pound.

machinist it right. It we look at weeks 24-26 you can see the peak.

.92*440 = 404.8
.90*450 = 405.0
.88*460 = 404.8

 

call me when you've got a geometry question...otherwise, i don't speak "math"