Answer:
<em>R(x) = (4.50 – 0.50x)(700 + 100x)</em>
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R(x) is in factored form
Where x is each decrease in the price.
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Explanation:
R(x) is in the form ax² + bx + c.
This is where the equation is distributed and simplified [Standard form]
The maximum revenue is represented by
R(-b/2a), where the vertex of this relationship is, at x = -b/2a.
Revenue = (Price)(Quantity)
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R(x) = (4.50 – 0.50x)(700 + 100x) →
<u>-50</u>x² + <u>100</u>x + <u>3150</u> [ax² + bx + c].
x = -b/2a
x = -(<u>100</u>)/2(<u>-50</u>)
x = -100 / -100
x = 100 / 100
x = 1
Therefore R(1) or where the price is decreased by a factor of 1 is the maximum revenue.
R(2) = -50(1)² + 100(1) + 3150
R(2) = -50(1) + 100 + 3150
R(2) = -50 + 100 + 3150
R(2) = 3200.
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Thus the best revenue ($3,200) is obtained by decreasing the price once (Price of 4$), with 800 cones.
