An economist modeled the demand Q for a certain product as a linear function of the selling price p the demand was 20000 units when the selling price was $40 per unit and the demand was 15,000 units when the selling price was $60 per unit based on the model what is the time and in units when the selling price is $55 per unit

The demand is 17000 units when the selling price is $55 per unit

A linear equation is in the form:

y = mx + b

where y, x are variables, m is the rate of change and b is the initial value of y.

Let Q represent the demand and P represent the selling price.

20000 units for selling price of $40, hence (40, 20000). 16000 units for selling price of $60, hence (60, 16000).

Hence:

For P = 55 unit:

W

Q = -200(55) + 28000 = 17000

The demand is 17000 units when the selling price is $55 per unit

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16,250 units.

Step-by-step explanation:

This is a linear function which means that it takes the form of y = mx + c.

Y is the demand

X is the price

Find m.

= (Y₂ - Y₁) / (X₂ - X₁)

= (15,000 - 20,000) / (60 - 40)

= -250

Find c using substitution;

20,000 = -250 * 40 + c

20,000 = -10,000 + c

c = 20,000 + 10,000

c = 30,000

Linear function is;

y = -250x + 30,000

If selling price is $55;

y = -250 * 55 + 30,000

y = 16,250 units.

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