Supply and demand equation

Question

An important application of systems of equations arises in connection with supply and demand. As the price of a product​ increases, the demand for that product decreases.​ However, at higher​ prices, suppliers are willing to produce greater quantities of the product. The price at which supply and demand are equal is called the equilibrium price. The quantity supplied and demanded at that price is called the equilibrium quantity. The following demand and supply models describe prices for unleaded premium​ gasoline, where p is the price of gasoline​ (per gallon). Use the models below to complete parts​ (a) and​ (b).

Demand​ Model:

p=−0.002x+4.3​; x is the number of gallons demanded per day.

Supply​ Model:

p=0.005x+0.8​; x is the number of gallons supplied per day.

Answer 1

-0.002x + 4.3 = 0.005x + 0.8

.007x = 3.5

x = 3.5/.007 = 500 gallons per day

x=500 = equilibrium output level of production

p = .005(500) +.8 = 2.5 + .8 = 5.3 = equilibrium price = $5.30 per gallon (in California lately)

p = -.002(500) + 4.3 = 5.3