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

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windyyork windyyork · Answer 1 · 2020-04-06T09:07:59+02:00

Answer: The weekly demand equation would be

[tex]p=-0.2m+84.8[/tex]

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

[tex]p=mx+b\\\\63=109m+b\\\\63-109m=b-----------------(1)[/tex]

If p = $12.80, x= 360

So, the equation of price would be

[tex]12.80=360m+b\\\\12.80-360m=b-------------(2)[/tex]

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

[tex]63-109m=12.80-360m\\\\63-12.80=-360m+109m\\\\50.20=-251m\\\\\dfrac{50.2}{251}=-m\\\\-0.2=m[/tex]

So, the value of b would be

[tex]63=109m+b\\\\63-109(-0.2)=b\\\\63+21.8=b\\\\84.8=b[/tex]

So, the weekly demand equation would be

[tex]p=-0.2m+84.8[/tex]