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=−0.007x+15.1; x is the number of gallons demanded per day. Supply Model: p=0.003x+0.1; x is the number of gallons supplied per day. a. Solve the system and find the equilibrium quantity and the equilibrium price for a gallon of unleaded premium gasoline. The equilibrium quantity for a gallon of unleaded premium gasoline is__gallons. (Type a whole number.) Part 2 The equilibrium price for a gallon of unleaded premium gasoline is $ (Type an integer or a decimal.) Part 3 b. Use the answers from part (a) to complete the following statement. If unleaded premium gasoline is sold for $_ per gallon, there will be a demand for_gallons per day and___gallons will be supplied per day. (Type integers or decimals.)

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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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=−0.007x+15.1; x is the number of gallons demanded per day.

Supply Model: p=0.003x+0.1; x is the number of gallons supplied per day.

a. Solve the system and find the equilibrium quantity and the equilibrium price for a gallon of unleaded premium gasoline.

The equilibrium quantity for a gallon of unleaded premium gasoline is____gallons.

(Type a whole number.)