Question

When the price of a product is p dollars​ each, suppose that a manufacturer will supply 2p-12 units of the product to the market and that consumers will demand to buy 270-4p units. At the value of p for which supply equals​ demand, the market is said to be in equilibrium. Find this value of p.

Answer 1

Answer:

$p=47$

Step-by-step explanation:

We have been given that when the price of a product is p dollars​ each, suppose that a manufacturer will supply $2p-12$ units of the product to the market and that consumers will demand to buy $270-4p$ units. We are asked to find the equilibrium.

To find equilibrium, we will equate demand with supply and solve for p as:

$2p-12=270-4p$  

$2p+4p-12=270-4p+4p$

$6p-12=270$

$6p-12+12=270+12$

$6p=282$

$\frac{6p}{6}=\frac{282}{6}$

$p=47$

Therefore, when the price of product is $47, then the market is said to be in equilibrium.