Question

HI can you help me with this problem?The quantity demanded x for a certain brand of MP3 players is 300 units when the unit price p is set at $90. The quantity demanded is 1300 units when the unit price is $40. Find the demand equation

Answer 1

The demand equation is P = -0.05x + 105

STEP - BY - STEP EXPLANATION

What to find?

The demand equation.

The following information is used to solve the problem.

If (x₁ , y₁) and (x₂, y₂) are any dinstinct points on a line a non-vertical line L, then the equation of the line that has a slope(m) and passes through the point (x₁ , y₁) is given by the formula below:

`y-y_1=_{}(y_2-y_1)/(x_2-x_1)(x-x_1)`

Assume p, be the unit price and x be the demand when the price is $p.

From the question given, when the unit price x = 300 units, the demand p = $90 and when the unit price x = 1300 units, the demand p = $40

This means the demand curve passes through the points (300, 90) and (1300, 40).

Assume the demand equation is linear, then the line of the equation passes through the points (300, 90) and (1300, 40).

Now;

y=p x₁ =300 y₁ = 90 x₂ = 1300 y₂=40

Substitute the values into the function and simplify.

`p-90=(40-90)/(1300-300)(x-300)`

Simplify the above.

`p-90=(-50)/(1000)(x-300)`
`p-90=-0.05(x-300)`

Open the parenthesis.

P- 90 = -0.05x + 15

Add 90 to both-side of the equation.

P = -0.05x + 15 + 90

P = -0.05x + 105

Hence, the demand function is P = -0.05x + 105