Question

Suppose a certain home improvement outlet knows that the monthly demand for framing studs is 2,300 when the price is $4.77 each but that the demand is 3,300 when the price is $4.67 each. Assuming that the demand function is linear, write its equation. Use p for price (in dollars) and q for quantity?

Answer 1

Answer:

p + 0.0001q = 5

Step-by-step explanation:

Data provided in the question:

When Price, p₁ = $4.77 ; Demand, q₁ = 2,300

and,

When Price, p₂ = 3,300 ; Demand, q₂ = 3,300

considering the above as the points on the line,

now, the general equation for a line is given as:

$\frac{q_1-q}{p_1-p}=\frac{q_2-q_1}{p_2-p_1}$

on substituting the respective values, we get

$\frac{2,300-q}{4.77-p}=\frac{3,300-2,300}{4.67-4.77}$

or

$\frac{2,300-q}{4.77-p}=\frac{1000}{-0.1}$

or

2,300 - q = -10,000(4.77 - p)

or

⇒ 2,300 - q = -47700 + 10,000p

or

⇒ 10,000p + q = 2300 + 47700

or

⇒ 10,000p + q = 50000

or

⇒ p + 0.0001q = 5