Saturday 6 November 2021

Suppose that the supply and demand equations for printed​ T-shirts for a particular week are given as​ follows, where p is the price in dollars and q is the quantity in hundreds.

 Suppose that the supply and demand equations for printed​ T-shirts for a particular week are given as​ follows, where p is the price in dollars and q is the quantity in hundreds.

 

​(A) Find the supply and demand​ (to the nearest​ unit) if​ T-shirts are $ 7 each.
To find the​ supply, substitute $ 7 for p into the​ price-supply equation and solve for q. Because the quantity is measured in​ hundreds, multiply the resulting value by 100 to find the number of units.
Substitute ​$7 for p into the​ price-supply equation and solve for​ q, rounding to two decimal places.

 

 

​(C) Find the equilibrium price and quantity.
In this​ scenario, the intersection of the graphs of the​ price-supply and​ price-demand equations represents the equilibrium price and quantity.
Find the equilibrium price and quantity. Substitute the second equation into the first equation and solve for q to find the value of q at the point of intersection rounded to two decimal places. 

 

​(D) Graph the two equations in the same coordinate system and identify the equilibrium​ point, supply​ curve, and demand curve.
The graph is shown to the right.


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