Question

The daily demand for ice cream cones at a price of$1.20 per cone is 50 cones. At aprice of$2.20 per cone, the demand is 30 cones. Use linear interpolation to estimatethe demand at a price of$1.50 per cone.Summary:

Answer 1

Using linear interpolation, the estimated demand for ice cream cones at a price of $1.50 per cone is calculated to be 44 cones.

Step-by-step explanation:

To estimate the demand at a price of $1.50 per cone using linear interpolation, we need to create a straight line between the two known points: (1.20, 50) and (2.20, 30), where the first value in each pair is the price per cone, and the second value is the demand.

The formula for the line can be found using:

Demand Change = (Demand at High Price - Demand at Low Price) / (High Price - Low Price)

Interpolated Demand = Demand at Low Price + (Demand Change) * (Interpolated Price - Low Price)

The Demand Change is:

(30 - 50) cones / ($2.20 - $1.20) = -20 cones / $1.00 = -20 cones/$

Plugging in the values to estimate the demand at $1.50 per cone:

Interpolated Demand = 50 cones + (-20 cones/$) * ($1.50 - $1.20)

Interpolated Demand = 50 cones - 6 cones

Interpolated Demand = 44 cones

Thus, at a price of $1.50 per cone, the estimated demand for ice cream cones is 44 cones.