Question

Suppose a publishing company estimates that its monthly cost is C(x) = 600{x^2} + 300xC(x)=600x 2 +300x and its monthly revenue is R(x) = - 0.4{x^3} + 700{x^2} - 600x + 500R(x)=−0.4x 3 +700x 2 −600x+500, where x is in thousands of books sold. The profit is the difference between the revenue and the cost.
What is the profit function, P(x)?​

Answer 1

Answer:

the answer is A,

P(x) = -0.4x³+100x²-900x+500

Step-by-step explanation:

monthly cost:

$c(x) = 600x {}^{2} + 300x$

monthly revenue:

$r(x) = - 0.4 {}^{3} + 700x {}^{2} - 600x + 500$

profit function:

$p(x) = r(x) - c(x)$

$p(x) = ( - 0.4x {}^{3} + 700 {x}^{2} - 600x + 500) - (600x {}^{2} + 300x)$

i) remove the first bracket

$p(x) = - 0.4x {}^{3} + 700x {}^{2} - 600x + 500 - (600 {x}^{2} + 300x)$

ii) there is a negative sign, '-' in front of the second bracket. so, change the sign of each term of the expression inside the bracket

$p(x) = - 0.4x {}^{3} + 700 {x}^{2} - 600x + 500 - 600x {}^{2} - 300x$

iii) collect like terms

$p(x) = - 0.4x {}^{3} + 700 {x}^{2} - 600 {x}^{2} - 600x - 300x + 500$

iv) simply the like terms

$p(x) = - 0. 4{x}^{3} + 100 {x}^{2} - 900x + 500$