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

(a)
`R(x)=410x-(x^(2))/(6)`

(b) profit = 95,683.33

Step-by-step explanation:

`Price:p(x)=410-(x)/(6)`

C(x) = 5900 + 130 x

(a) Revenue, R(x) = Price × Quantity

`=410-(x)/(6)* x`

`=410x-(x^(2))/(6)`

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

`=410x-(x^(2))/(6)-5900 - 130x`

At x = 1150

`=410(1150)-(1150^(2) )/(6)-5900-130(1150)`

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

= 95,683.33