Question

Country Workshop manufactures both finished and unfinished furniture for the home. The estimated quantities demanded each week of its rolltop desks in the finished and unfinished versions are x and y units when the corresponding unit prices in dollars, p and q, respectively, are described in the following equations.p = 200 - 1/5 x - 1/10 yq = 160 - 1/10 x - 1/4 yFor the weekly total revenue function R(x, y), compute the values of R listed below using the given unit prices.R(80, 40) = $R(60, 100) = $

Answer 1

[tex] R(80,40)=322 [\tex]

Explanation:

We have [tex] R(x,y)=p(x,y)+q(x,y) [\tex] because is the weekly total revenue function. If [tex] R(x,y)=R(80,40) [\tex], then we have,

[tex] x=80 [\tex]:

[tex] y=40 [\tex]:

And also we have,

[tex] p=200 -\frac{1}{5}x -\frac{1}{10}y [\tex]

[tex] p=200 -\frac{80}{5} -\frac{40}{10} [\tex]

[tex] p=200 -16 -4 [\tex]

[tex] p=180 [\tex]

and,

[tex] q=160 -\frac{1}{10}x -\frac{1}{4}y [\tex]

[tex] q=160 -\frac{80}{10} -\frac{40}{4} [\tex]

[tex] q=160 -8 -10 [\tex]

[tex] q=142 [\tex]

Then [tex] R(80,40)=180+142=322 [\tex], that means that Country Workshops earns 322 dollars per month under those conditions.

Analogously, If [tex] R(x,y)=R(60,100) [\tex] then [tex] p=178, q=129 [\tex], and [tex] R(60,100)=178+129=307 [\tex]. Country Workshops earns 307 dollars per month under those new conditions.