The quantity demanded x of a certain brand of DVD player is 3000/week when the unit price p is $485. For each decrease in unit price of $20 below $485, the quantity demanded increases by 250 units. The suppliers will not market any DVD players if the unit price is $350 or lower. But at a unit price of $525, they are willing to make available 2500 units in the market. The supply equation is also known to be linear.

Question

The quantity demanded x of a certain brand of DVD player is 3000/week when the unit price p is $485. For each decrease in unit price of $20 below $485, the quantity demanded increases by 250 units. The suppliers will not market any DVD players if the unit price is $350 or lower. But at a unit price of $525, they are willing to make available 2500 units in the market. The supply equation is also known to be linear.

Answer 1

To find the supply equation, we can use the information given. We know that at a unit price of $525, the quantity supplied is 2500 units. We also know that the suppliers will not market any DVD players if the unit price is $350 or lower.

Let's assume the supply equation is in the form:

Qs = mP + b

where Qs is the quantity supplied, P is the unit price, m is the slope (rate of change of quantity with respect to price), and b is the y-intercept (quantity when the price is zero).

We can use the two points (525, 2500) and (350, 0) to find the slope (m) and the y-intercept (b) of the supply equation.

Using the slope formula:

m = (change in quantity)/(change in price)

m = (2500 - 0)/(525 - 350)
m = 2500/175
m = 14.286

Now that we have the slope (m), we can plug it into the equation:

Qs = 14.286P + b

Using the point (525, 2500), we can find the y-intercept (b):

2500 = 14.286(525) + b
2500 = 7500 + b
b = 2500 - 7500
b = -5000

Therefore, the supply equation for this particular DVD player is:

Qs = 14.286P - 5000