Question

the profit from the production and sale of music players is given by the function ( p(x) = 850x - 0.1x^2 - 4500 ), where ( x ) is the number of units produced and sold.

a. what is ( p(500) )? interpret this result.

b. what is the profit from the production of 8000 units? write this in functional notation.

Explanation:

Step1: Substitute x=500 into P(x)

$P(500) = 850(500) - 0.1(500)^2 - 4500$

Step2: Calculate each term

$850(500)=425000$, $0.1(500)^2=0.1(250000)=25000$

Step3: Compute final value for P(500)

$P(500) = 425000 - 25000 - 4500 = 395500$

Step4: Substitute x=8000 into P(x)

$P(8000) = 850(8000) - 0.1(8000)^2 - 4500$

Step5: Calculate each term

$850(8000)=6800000$, $0.1(8000)^2=0.1(64000000)=6400000$

Step6: Compute final value for P(8000)

$P(8000) = 6800000 - 6400000 - 4500 = 395500$

Answer:

a. $P(500)=395500$. This means the profit from producing and selling 500 music players is 395500 (in the relevant currency unit).
b. $P(8000)=395500$