Answer: The weekly demand equation would be
![p=-0.2m+84.8](https://tex.z-dn.net/?f=p%3D-0.2m%2B84.8)
Step-by-step explanation:
Since we have given that
Number of units of their portable media player = 109 units per week
Cost per unit = $63.00
At unit price of $12.80, consumer are buying 360 units per week.
So, here, p = $63.00 and x = 109 units
Here, price and quantity are linearly related by
![p=mx+b\\\\63=109m+b\\\\63-109m=b-----------------(1)](https://tex.z-dn.net/?f=p%3Dmx%2Bb%5C%5C%5C%5C63%3D109m%2Bb%5C%5C%5C%5C63-109m%3Db-----------------%281%29)
If p = $12.80, x= 360
So, the equation of price would be
![12.80=360m+b\\\\12.80-360m=b-------------(2)](https://tex.z-dn.net/?f=12.80%3D360m%2Bb%5C%5C%5C%5C12.80-360m%3Db-------------%282%29)
From eq(1) and (2), we get that
![63-109m=12.80-360m\\\\63-12.80=-360m+109m\\\\50.20=-251m\\\\\dfrac{50.2}{251}=-m\\\\-0.2=m](https://tex.z-dn.net/?f=63-109m%3D12.80-360m%5C%5C%5C%5C63-12.80%3D-360m%2B109m%5C%5C%5C%5C50.20%3D-251m%5C%5C%5C%5C%5Cdfrac%7B50.2%7D%7B251%7D%3D-m%5C%5C%5C%5C-0.2%3Dm)
So, the value of b would be
![63=109m+b\\\\63-109(-0.2)=b\\\\63+21.8=b\\\\84.8=b](https://tex.z-dn.net/?f=63%3D109m%2Bb%5C%5C%5C%5C63-109%28-0.2%29%3Db%5C%5C%5C%5C63%2B21.8%3Db%5C%5C%5C%5C84.8%3Db)
So, the weekly demand equation would be
![p=-0.2m+84.8](https://tex.z-dn.net/?f=p%3D-0.2m%2B84.8)