SOLUTION: Please help. The demand for cabinets depends on the price per cabinet. A manufacturer determines that the number of cabinets he can sell is d= -3p^2 + 114p-240, where p is the pric

Question 139750: Please help. The demand for cabinets depends on the price per cabinet. A manufacturer determines that the number of cabinets he can sell is d= -3p^2 + 114p-240, where p is the price per cabinet in dollars. At what price will the demand for cabinets be at a maximum?
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
Your equation is in the form with the value of a negative. This means you have a parabola that opens downward and that means that the vertex is the maximum point. The x-cordinate (actually the p-cordinate in this case) is the value of the independent variable that produces the maximum function value. So all you need to do to answer this question is find this value for the independent variable. This is easily calculated from the coefficients in the given equation. In general, the x-cordinate of the vertex is . For your equation, and . Just substitute and do the arithmetic
RELATED QUESTIONS
I'm really having trouble solving this question. 1. Sabrina wants to start cabinet... (answered by rothauserc)

Problem: The owner of a health foods store determines that the demand equation for... (answered by stanbon)

A company has a work force of 21 men that produces two types of top end cabinets.... (answered by josmiceli)

The owner of a health foods store determines that the demand equation for selling a... (answered by stanbon)

Please help me to find the value of p. When the price of a product is p dollars each,... (answered by htmentor)

This one is set up like a word problem and I could use some assistance. A company... (answered by ankor@dixie-net.com)

The demand for a certain product depends on the price. When the price is £10, £15 and... (answered by ikleyn)

let p=0.09q + 50 be the supply equation for a manufacturer. the demand equation for his... (answered by JoelSchwartz)

A furniture shop refinishes cabinets. Employees use one of two methods to refinish each... (answered by mananth)