Question

Country Workshop manufactures both

finished and unfinished furniture for the home . The
estimated quantities demanded each week of its roll top desks in
the finished and unfinished versions are x and y units when
the corresponding unit prices are
p=200−15x−110y

q=160−110x−14y

dollars, respectively. What is the weekly total revenue function R(x, y)?

Answer 1

The weekly total revenue function is
`R(x,y)=200x-15x^2-220xy+160y-14y^2`.

Explanation:

Let the estimated quantities demanded each week of its roll top desks in

the finished and unfinished versions are x and y units respectively.

The unit price of finished furniture is

`p=200-15x-110y`

The unit price of unfinished furniture is

`q=160-110x-14y`

Total weekly revenue function is

`R(x,y)=px+qy`

`R(x,y)=(200-15x-110y)x+(160-110x-14y)y`

`R(x,y)=200x-15x^2-110xy+160y-110xy-14y^2`

Combine like terms.

`R(x,y)=200x-15x^2+(-110xy-110xy)+160y-14y^2`

`R(x,y)=200x-15x^2-220xy+160y-14y^2`

Therefore the weekly total revenue function is
`R(x,y)=200x-15x^2-220xy+160y-14y^2`.