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.
Accepted Solution
A:
Answer:The demand of the desk is 4000 unitsStep-by-step explanation:From the question we know that p is equals negative x squared plus 23, that can be written as:[tex]p=-x^{2} +23[/tex]Where p is the unit price and x represent the quantity demanded in thousands. Replacing p by 7 and solving for x, we get:[tex]7=-x^{2} +23\\x^{2} =23-7\\x^{2} =16\\x=\sqrt{16\\} \\x=4[/tex]Since x is given in thousands of units, if the price is $7, the demand of the desk is 4000 units.