Question

An ice cream shop sells 700 cones per day at a price of $4.50. A survey lets the owner know

Answer 1

Answer:

R(x) = (4.50 – 0.50x)(700 + 100x)

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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) →

-50x² + 100x + 3150 [ax² + bx + c].

x = -b/2a

x = -(100)/2(-50)

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.