Question

Total profit P is defined as total revenue R -= total cost​ C, and is given by the function Upper P left parenthesis x right parenthesis equals Upper R left parenthesis x right parenthesis minus Upper C left parenthesis x right parenthesis. Find the total profit​ P(x) when ​R(x)equals150.97 x minus 0.3 x squared and Upper C left parenthesis x right parenthesis equals 4529.10 plus 0.5 x squared.

Answer 1

Explanation:

P(x) = R(x) - C(x)

Where,

P(x) = Total profit

R(x) = Total revenue

C(x) = Total cost

R(x)equals150.97 x minus 0.3 x squared

R(x) = 150.97x - 0.3x^2

Upper C left parenthesis x right parenthesis equals 4529.10 plus 0.5 x squared.

C(x) = 4529.10 + 0.5x^2

P(x) = R(x) - C(x)

= (150.97x - 0.3x^2) - ( 4529.10 + 0.5x^2)

= 150.97x - 0.3x^2 - 4529.10 - 0.5x^2

= 150.97x - 0.8x^2 - 4529.10

P(x) = -0.8x^2 + 150.97x - 4529.10