Carcass wrote:
A business is currently selling 30 chairs per day for a price of $25 per chair. A worker predicts that if the business chooses to lower the cost of the chairs, then for every $1 the price is lowered, one more chair will be sold. If the prediction is accurate, what is the maximum revenue the business can earn in a day from selling chairs? (Revenue is the amount of money that the business takes in, without consideration of expenses or other costs.)
Revenue = (Number of chairs)(cost per chair)
Currently,
R=(30)(25)=750As per the prediction,
R=(30+x)(25−x), where
x=1,2,3,......Now,
R1=(31)(24)=744R2=(32)(23)=736R3=(33)(22)=726We can see the values are decreasing, so the Maximum revenue could be
750 only
Alternative Approach:Let's solve the quadratic,
R=(30+x)(25−x)R=−x2−5x+750Parabola is a quadratic function with the maximum value at the vertexx-coordinate of the vertex is given by
−b2a=−(−5)(2)(−1)=−52This means - Maximum revenue would be generated if the number of chairs are
27.5 and the cost per chair is
27.5 too, which is not possible!