An ice cream shop sells 700 cones per day at a price of $4.50. A survey lets the owner know that for every decrease in price of $0.50, they will be able to sell 100 extra cones. Write an
equation for the Revenue, R, which can be used to determine how much the owners should
charge in order to maximize their revenue.​

R(x) = (4.50 – 0.50x)(700 + 100x)

R(x) is in factored form

Where x is each decrease in the price.

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)

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.

Thus the best revenue ($3,200) is obtained by decreasing the price once (Price of 4$), with 800 cones.

easy its decreasing

step-by-step explanation:

because its top point is at the to of the graph on the left side (atleast from the veiw i see it) now if that top point wast in the lower part of the graph it would be increasing hope this have a nice day