Question

Based upon market research, the Hawthorne Company has determined that consumers are willing to purchase 109 units of their portable media player each week when the price is set at $63.00 per unit. At a unit price of $12.80, consumers are willing to buy 360 units per week. (a) Determine the weekly demand equation for this product, assuming price, p, and quantity, x, are linearly related. p

Answer 1

Answer: The weekly demand equation would be

`p=-0.2m+84.8`

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)`

If p = $12.80, x= 360

So, the equation of price would be

`12.80=360m+b\\\\12.80-360m=b-------------(2)`

From eq(1) and (2), we get that

`63-109m=12.80-360m\\\\63-12.80=-360m+109m\\\\50.20=-251m\\\\(50.2)/(251)=-m\\\\-0.2=m`

So, the value of b would be

`63=109m+b\\\\63-109(-0.2)=b\\\\63+21.8=b\\\\84.8=b`

So, the weekly demand equation would be

`p=-0.2m+84.8`