I need help i don’t understand and i have limited time

[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.