B RIEF C ALC – S EM 1 R EVIEW C H 1 Formulas: Three forms of Linear Equations Standard: Ax + By = C “A” and “ B ” must be a whole numbers “A” must be positive.

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B RIEF C ALC – S EM 1 R EVIEW C H 1 Formulas: Three forms of Linear Equations Standard: Ax + By = C “A” and “ B ” must be a whole numbers “A” must be positive Slope-Intercept: y = mx + b Point-slope: y – y 1 =m(x – x 1 ) Cost/Profit/Supply/Demand/Revenue: P = R - C Break- even/ Market Price: Supply = Demand

W- UP B RIEF - C ALC CH 1 1.Write an equation in general form perpendicular to the line 6x – 2y = -5 containing the point (-1,-2) 2.Write an equation in general form parallel to the line x – 2y = -5 containing the point (8, -10) 3.Starbucks pays a fixed cost to produce cases of coffee of $40 plus $6 for each one produced. They sell each case to their stores for $30. a)Find cost equationb) Find revenue equation c) Find profit equation Answers: 1. x + 3y = x + 2y = C = 6x + 40 R = 30x P = 24x - 40

C HAPTER 2 1. solve using any method 3x +3y +2z = 4 x – 3y +z = 10 5x – 2y – 3z = 8 2. Determine the number of solutions (one, none or infinite). x – y – z = 1 2x +3y +z = 2 3x + 2y = 0 3 Use the matrix to the left. Answers: 1. (2, -2,2) 2. none 3. [7/8, ½ 1/8] 4. [ ½ -1 ½ ]

a b c d B RIEF - C ALC R EVIEW C H 3 1.Determine which region in the graph to the right represents the equations 2x – 5y < -5 and 3x + 5y < What point would maximize the objective function z = 5x + 7y subject to: x + y >2 x+ y 0 y > 0 3.Write the constraints and profit for the following… A farmer has 70 acres of land available on which he grows soybeans and corn. The cost of cultivation per acre for soybeans is $60 and $30 for corn. The workdays needed per acre for corn is 4 days and 3 days for soybeans. The farmer has $1800 for cost and 120 days to cultivate the crops. He makes $300 profit per acre of soybeans and $150 per acre of corn. Find the number of acres of each he should plant to maximize his profit. Answers: 1. b 2. (0,8) x + y < 70 60x + 30y < x + 4y < 120 P = 300x + 150y