Maximizing profit equation

[slab_ryda]

Maximizing profit equation URGENT

1. Homework Statement :
A goat salesman can sell 12 goats per day at a price of 15000 each. His marketing dept estimates that for each $300 price reduction he can sell 2 more goats per day. If each goat costs him $12000, and fixed costs are $1000, use calculus to determine what price he should charge to maximize his profit? How many goats will he sell at this price? (hint! Let x be the number of $300 price reductions.)


2. Homework Equations :

?

3. The Attempt at a Solution :

I started off with p-15000= [(15000-300)/(12-14)] (x-12)

which, after deriving and equating p' to 0 ; i got x= 7.02




My issue:

I honestly don't think i got the first equation right. I've tried thinkin outside the box on this one, but i have a feeling that its much easier than I am making it out to be in my own head. This problem is for a group assignment and I can't let my group down. I asked my math tutor, but she's totally useless for application problems involving business.




Thank you to anyone for any help/ attempting to help :) :)

ps. i would usually find a more competent tutor or ask my school's tutor, but its crunch time on the day before the group thing is due, so I am kinda stuck between a rock and this math problem.

 

[Dick]

Break the problem down into parts and express each as a function of x. i) how many goats do you sell per day and ii) what's the price of each goat. Try to combine those into an expression with the other facts to get an expression for profit.

 

[slab_ryda]

express each as a function of the number of price reductions? Is that what you are saying? or just x as a variable

 

[Dick]

express each as a function of the number of price reductions? Is that what you are saying? or just x as a variable

Yes, x as the number of price reductions. Follow the hint. "just x as a variable" doesn't mean much. So answer my questions i) and ii).

 

[slab_ryda]

This is probably a very easy easy question, but I am kinda stumped on how to figure it out. even your Q's i) and ii), Dick, please excuse my stupidity, i just want to solve it so my group doesn't take a fall.

 

[Dick]

This is probably a very easy easy question, but I am kinda stumped on how to figure it out. even your Q's i) and ii), Dick, please excuse my stupidity, i just want to solve it so my group doesn't take a fall.

You can't figure out an expression for number of goats sold per day if x is the number of price reductions?? The only way not to let your group down is to figure this out. Let's call that expression GPD. If x=0, the GPD=12. If x=1, then GPD=14. If x=2, then GPD=16. This is easy.