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**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.)

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 dont 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 im 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 shes 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 im kinda stuck between a rock and this math problem.