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

the answer is A,

P(x) = -0.4x³+100x²-900x+500

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`