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) = $

Question

Mathematics

Catherine Dunn

2 May, 08:45

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) = $

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Kathy Moyer · Answer 1

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

Step-by-step 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.