what is the value?

Question

the profit (P), in dollars, for a company is modeled by the function P(x)= -750x^2 + 15,000x, where is x the number of items produced. For which values of x will the company lose money?

 

 

A. x < 2

B. 10 ≤ x < 20

C. 2 < x ≤ 10

D. x > 20

Answer 1

The answer is any value of x that is greater than 20. One way to solve this is to find the value of x where P=0. To do this you simply set the function equal to zero and solve for x: -750x^2+15,000x=0. You can pull out 750x from both parts of the function: 750x(-x+20)=0. Now you can solve for x by setting 750x=0 and (-x+20)=0. This means that P=0 at the values x=0 and x=20. This means the company is profitable between x=0 and x=20, and since the company cannot make a negative quantity, the company will only loose money if x>20. One way to check this is by plugging in a number greater than 20 into the profit function. An example of which is 21. P=-750(21)^2+15,000(21). In this example P=-330,750+315,000=-1570. Now you have proven that a value greater than 20 produces a loss.