Question

A common equation used in business is a demand equation. It expresses the relationship between the unit price of some commodity and the quantity demanded. In the​ equation, p represents the unit price and x represents the quantity demanded in thousands. A company sells desk lamps and has found that the demand equation for a certain style of desk lamp is given by the equation p equals negative x squared plus 23. Find the demand for the desk lamp if the price is ​$7 per lamp.

Answer 1

The demand of the desk is 4000 units

Explanation:

From the question we know that p is equals negative x squared plus 23, that can be written as:

`p=-x^(2) +23`

Where p is the unit price and x represent the quantity demanded in thousands. Replacing p by 7 and solving for x, we get:

`7=-x^(2) +23\\x^(2) =23-7\\x^(2) =16\\x=√(16\\) \\x=4`

Since x is given in thousands of units, if the price is $7, the demand of the desk is 4000 units.