the function c(x) = 600x – 0.3x2 represents total costs for a company to produce a product, where c is the total cost in dollars and x is the number of units sold. what number of units would produce a maximum cost? what is the maximum cost?

1000 number of units would produce maximum cost.

Maximum cost = 300000

Step-by-step explanation:

Given that total costs for a company to produce a product x as C(x) = 600x – 0.3x²

At maximum cost derivative of C(x) is zero.

        C'(x) = 600 – 0.6x = 0

        0.6x = 600

            x = 1000

1000 number of units would produce maximum cost.

Maximum cost = C(1000) = 600 x 1000 – 0.3 x 1000² = 300000

answer is 8x+24

area of vanessa's patio = length × width

given, length = (3x² + 5x + 10)

width = (x² - 3x - 1)

area of vanessa's patio = (3x² + 5x + 10)(x² - 3x - 1)

= 3x²(x² - 3x - 1) + 5x(x² - 3x - 1) + 10(x² - 3x - 1)

= 3x⁴ - 9x³ - 3x² + 5x³ - 15x² - 5x + 10x² - 30x - 10

= 3x⁴ - 4x³ - 8x² - 35x - 10

hence, expression of vanessa's patio = (3x⁴ - 4x³ - 8x² - 35x - 10)