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.

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

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

[tex]2p-12=270-4p[/tex]

[tex]2p+4p-12=270-4p+4p[/tex]

[tex]6p-12=270[/tex]

[tex]6p-12+12=270+12[/tex]

[tex]6p=282[/tex]

[tex]\frac{6p}{6}=\frac{282}{6}[/tex]

[tex]p=47[/tex]

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

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.

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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.