At a price of 221 per bushel the supply of a certain grains

At a price of $2,21 per bushel the supply of a certain grains is 7400 million bushels and the demanded is 7500 million bushels. At a price of $2.32 per bushel, the supply is 7800 million bushels and the demand is 7400 million bushels. Find a price-supply equation of the from p = mx + b, where p is the price in dollars and x is the supply in millions of bushels. Find a price-demand equation of the from p = mx + b, where p is the price in dollars and x is the demand in millions of bushels. Find the equilibrium point. Graph the price-supply equation, price-demand equation, and equilibrium point in the same coordinate system. The price-supply equation is p = (Type an exact answer)

Solution

Solution :

( a ) Price-Supply :
(7400, 2.21) , (7800, 2.32)

slope = 0.11/400 = 0.000275

y - 2.21=0.000275(x - 7400)

y = 0.000275x + 0.175

( b ) Price-Demand :

(7500,2.21) , (7400,2.32)

slope=0.11/-100 = - 0.001

y - 2.21= - 0.001(x - 7500)  

y = - 0.001x + 9.71

( c )

     Equilibrium Point (intersection)

y(supply) = y(demand)

0.000275x + 0.175 = - 0.001x + 9.71

0.001275x = 9.535

x = 7478.43

y = - 0.001(7478.43) + 9.71 = 2.232

y = 2.232

(7478.43,2.23)