Question

Producers of a certain brand of refrigerator will make 1000 refrigerators available when the unit price is $260. At a unit price of $300, 5000 refrigerators will be marketed. Find the equation relating the unit price p of a refrigerator to the quantity supplied x if the equation is known to be linear.

Answer 1

The linear equation is;

Δx=100.Δp

Step-by-step explanation:

Step 1: Derive the linear equation

The linear equation can be expressed as;

Δx=Δp×k

where;

Δx=change in quantity supplied

Δp=change in unit price

k=constant of proportionality

Step 2: Substitute values in the equation

Δx=final quantity-initial quantity

where;

final quantity=5,000

initial quantity=1,000

replacing;

Δx=5,000-1,000=4,000

Δp=final price-initial price

where;

final price=$300

initial price=$260

replacing;

Δp=300-260=$40

Step 4: Determine k

k=Δx/Δp=4000/40=100

Step 5: Linear equation

Δx/Δp=k

but k=100

Δx=100×Δp

Δx=100.Δp