Section 1.4 Intersection of Straight Lines

Intersection Point of Two Lines Given the two lines m 1,m 2, b 1, and b 2 are constants Find a point (x, y) that satisfies both equations. Solve the system consisting of L1L1 L2L2

Ex. Find the intersection point of the following pairs of lines: Notice both are in Slope-Intercept Form Substitute in for y Solve for x Find y Intersection point: (4, 9)

Break-Even Analysis The break-even level of operation is the level of production that results in no profit and no loss. Profit = Revenue – Cost = 0 Revenue = Cost Dollars Units loss Revenue Cost profit break-even point

Cost: C(x) = 3x Ex. A shirt producer has a fixed monthly cost of $3600. If each shirt has a cost of $3 and sells for $12 find the break-even point. If x is the number of shirts produced and sold Revenue: R(x) = 12x At 400 units the break-even revenue is $4800

Market Equilibrium Market Equilibrium occurs when the quantity produced is equal to the quantity demanded. price x units supply curve demand curve Equilibrium Point

Ex. The maker of a plastic container has determined that the demand for its product is 400 units if the unit price is $3 and 900 units if the unit price is $2.50. The manufacturer will not supply any containers for less than $1 but for each $0.30 increase in unit price above the $1, the manufacturer will market an additional 200 units. Both the supply and demand functions are linear. Let p be the price in dollars, x be in units of 100 and find: a. The demand function b. The supply function c. The equilibrium price and quantity

a. The demand function b. The supply function

c. The equilibrium price and quantity Solveand simultaneously. The equilibrium quantity is 960 units at a price of $2.44 per unit.