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18 August, 22:50

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.

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  1. 19 August, 00:30
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    The linear equation is;

    Δx=100.Δp

    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
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