Buying and Selling Beef Word Problem

[darshanpatel]

Homework Statement

A steer weighing 300 pounds gains 8 pounds per day and costs 1.00 dollar a day to keep. You bought this steer today at market price of 1.50 dollars per pound. However, the market price is falling 2 cents per pound per day. When should you sell the steer in order to maximize your profit?

Homework Equations

-None-

The Attempt at a Solution

Well, I figured out the basics but don't know where to go from there.

Total cost for steer: $450 ---> 1.50 dollars x 300 pounds
You lose $9 + $1= losing $10 per day ----> market falling 2 cents per day per pound + 1 dollar a day to keep

How does the gaining of 8 pounds per day come into play? Would it mean you increasing value of 8 pounds x 1.50 dollars per day = 12 dollars a day? But then it doesn't make sense as if you are gaining more than you lose, why sell?

Please help and any help is greatly appreciated.

 

[SteamKing]

Remember, the price of beef today is $1.50 per pound. In 10 days, the price drops to $1.30 per pound, but the steer now weighs 380 pounds.
You must write an equation which gives the profit on the sale of the steer as a function of days from the present time. There will be a point when profit is maximized, after which point the amount of profit declines due to the cost of feeding and keeping the steer while the sale price drops.

 

[darshanpatel]

oh that makes sense, so would the equation be .02x^2+8x+300=0 or something? I need help with that too

 

[SteamKing]

If x is the number of days from the present time, what equation would give the future weight of the steer, if the steer gains 8 pounds per day? Likewise, you can write another formula for the price of beef, and another which determines the cost of keeping the steer before selling it. The profit from the sale of the steer will be the price for the steer at sale minus the cost of keeping the steer.

 

[HallsofIvy]

Homework Statement

A steer weighing 300 pounds gains 8 pounds per day and costs 1.00 dollar a day to keep. You bought this steer today at market price of 1.50 dollars per pound. However, the market price is falling 2 cents per pound per day. When should you sell the steer in order to maximize your profit?

The weight of the steer, after "x" days will be 300+ 8x pounds. The market value will be 1.50- .02x dollars so you can sell it for a total of (300+ 8x)(1.50- .02x) dollars. That is the function you want to maximize.

 

[darshanpatel]

Ohhh that makes so much sense and that is what we have been learning. Thanks for the help!

 

[darshanpatel]

I am not getting the correct answer which is supposed to be about 16 days. I think you forgot about the cost to keep the steer is $1 a day and didn't factor that part in... How would you factor it in?I just figured it out but the correct formula would be (300+8x)(1.50-.02x)-x which gives you about 15.625 rounded= 16 days thanks for the help though