Question

The price-demand and cost functions for the production and sales x BBQ grills are given as p ( x ) = 410 − x / 6 C ( x ) = 5900 + 130 x The price p ( x ) and the cost C ( x ) are in dollars. a . Find the revenue function in terms of x . R ( x ) = b . Find the profit earned at an output of 1150 BBQ grills. Round to the nearest cent.

Answer 1

Answer:

(a)   $R(x)=410x-\frac{x^{2}}{6}$

(b) profit = 95,683.33

Explanation:

$Price:p(x)=410-\frac{x}{6}$

C(x) = 5900 + 130 x

(a) Revenue, R(x) = Price × Quantity

                    $=410-\frac{x}{6}\times x$

                    $=410x-\frac{x^{2}}{6}$

(b) profit = R(x) - C(x)

              $=410x-\frac{x^{2}}{6}-5900 - 130x$

                       At x = 1150

$=410(1150)-\frac{1150^{2} }{6}-5900-130(1150)$

= 471,500 - 220,416.67 - 5,900 - 149,500

= 95,683.33