# Pre-Calculus

The profit in dollars in producing x items of some commodity is given by the equation P=−11x2+346.5x−2612.5.
How many items should be produced to break even?(If there are two break-even points, then enter the smaller value of x. Your solution may not be an integer. Use your calculator for irrational square roots.)

I know that P(x)=revenue - cost, but I don't know how to set revenue and cost equal to each other to find break-even if they are already combined in −11x2+346.5x−2612.5...

1. 👍
2. 👎
3. 👁
1. The function is P=−11x^2+346.5x−2612.5

1. 👍
2. 👎
2. break-even is where profit=0.

1. 👍
2. 👎
3. I think your equation already contains revenue and cost, since it is labeled as "profit"
I interpret "break-even" point as having no loss or profit, or , P = 0
so we want the roots of
-11x^2 + 346.5x - 2612.5

x = (-346.5 ± √(5112.25)/-22
= 12.5 or 19

Wolfram confirms my answers
http://www.wolframalpha.com/input/?i=−11x%5E2%2B346.5x−2612.5%3D0+

1. 👍
2. 👎
4. Oh yeah I forgot it meant that P = 0 thanks

1. 👍
2. 👎

## Similar Questions

1. ### calculus

The net monthly profit, in dollars, from the sale of a certain item is given by the formula P(x) = 10^6[1 + (x-1)e^0.001x], where x is the number of items sold. a) Find the number of items that yield the maximum profit. At full

2. ### profit and loss

a businessman purchased certain items worth rs. 1200 and after selling some items at the end of the first day made a profit of 16 % on items sold on that day. if his profit for the day was 4 % of his total purchases what is his

3. ### pre-calculus

the profit of a company, in dollars, is the difference between the company's revenue and cost. the cost C(x), and R(x) are functions for a particular company. the x represents the number of items produced and sold to distributors.

4. ### Algebra II

The profit P, in dollars, gained by selling X computers is modeled by the equation P+-5X^2+1000x+5000. How many computers must be sold to obtain a profit of 55,000

1. ### Algebra

A print shop makes bumper stickers for election campaigns. If x stickers are ordered (where x < 10,000), then the price per sticker is 0.28 − 0.000002x dollars, and the total cost of producing the order is 0.087x − 0.0000005x2

2. ### Calculus

The cost (in dollars) of producing x units of a certain commodity is c(x)=5000+10x+0.05x^2 Find A=100 to x=105 so far i got y-y/x-x= C(105)-C(100)/105-105 i don't understand how it comes out to be 101.25/5 please help me

3. ### Math

A manufacturer estimates that the profit P from producing x units of a commodity is P=-x^2+40x-100 dollars per week. What is the maximium profit he can realize in one week? I was going to take the derivative of the equation and

4. ### Math

After experimentation, a certain manufacturer determined that if x units of a particular commodity are produced per week, the marginal cost is given by 0.3x -11, where the production cost is in dollars. If the selling price of the

1. ### math

Suppose the cost of producing x items is given by C(x)=1000-x^3, and the revenue made on the sale of x-items is R(x)=100x-10x^2. Find the number of items which serves as a break-even point.

2. ### Math - average rate problems(check + help)

The total cost, c, in dollars of operating a factory that produces kitchen utensils is C(x)=0.5x^2+40x+8000, where x is the number of items produced in thousands. a)Determine the marginal cost of producing 5000itmes and compare

3. ### Statistics

A manufacturer estimates that when x units of a particular commodity are produced each month, the total cost (in dollars) will be C(x) = 1/8x^2+4x+200 and all units can be sold at a price of p(x) = 49 - x dollars per unit.

4. ### analazye profit functions

For a certain company, the cost function for producing x items is C(x)=40x+150 and the revenue function for selling x items is R(x)=−0.5(x−80)2+3,200. The maximum capacity of the company is 100 items. The profit function P(x)