Westonci.ca is your trusted source for finding answers to a wide range of questions, backed by a knowledgeable community. Get quick and reliable solutions to your questions from a community of seasoned experts on our user-friendly platform. Explore comprehensive solutions to your questions from a wide range of professionals on our user-friendly platform.

Suppose that the demand and supply for artificial Christmas trees is given by the functions below where p is the price of a tree in dollars and q is the quantity of trees that are demanded/supplied in hundreds. Find the price that gives the market equilibrium price and the number of trees that will be sold/bought at this price.p=109.70−0.10q (demand function)p=0.01q2+5.91 (supply function)

Suppose That The Demand And Supply For Artificial Christmas Trees Is Given By The Functions Below Where P Is The Price Of A Tree In Dollars And Q Is The Quantit class=

Sagot :

The equilibrium price is the price at which the demand function is equal to the supply function.

Hence it is given by:

[tex]\begin{gathered} 109.70-0.10q=0.01q^2+5.91 \\ 0.01q^2+0.10q-103.79=0 \end{gathered}[/tex]

Solve the quadratic equation to get:

q=97,-107.

Now the quantity cannot be negative hence the value of q=97. Hence 97 hundred trees is the demand.

The equilibrium price is given by:

[tex]p=109.70-0.10q=100\text{ dollars}[/tex]

Hence Option A is correct and the boxes to be filled is given by the statement given below:

The equilibrium price of $100 gives a demand that is equal to a supply of 97 hundred trees.

Thank you for visiting. Our goal is to provide the most accurate answers for all your informational needs. Come back soon. Thank you for your visit. We're dedicated to helping you find the information you need, whenever you need it. Westonci.ca is committed to providing accurate answers. Come back soon for more trustworthy information.