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BRIEF CALC – SEM 1 REVIEW CH 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 – y1=m(x – x1) Cost/Profit/Supply/Demand/Revenue: P = R - C Break- even/ Market Price: Supply = Demand W-UP BRIEF- CALC 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 equation b) Find revenue equation c) Find profit equation Answers: 1. x + 3y = -7 2. x + 2y = 28 3. C = 6x + 40 R = 30x P = 24x - 40 CHAPTER 2 1. solve using any method 3x +3y +2z = 4 x – 3y +z = 10 5x – 2y – 3z = 8 1 4 3 4 1 8 0 0 1 2 1 4 1 4 1 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. 3. R3 r2 r3 4. R2 2r3 r2 Answers: 1. (2, -2,2) 2. none 3. [7/8, ½ 1/8] 4. [ ½ -1 ½ ] BRIEF- CALC REVIEW CH 3 1. Determine which region in the graph to the right represents the equations 2x – 5y < -5 a and 3x + 5y < 30 2. What point would maximize the objective function z = 5x + 7y subject to: x + y >2 2x + y < 10 x > 0 b x+ y < 8 y>0 d c 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) 56 3. x + y < 70 60x + 30y < 1800 3x + 4y < 120 P = 300x + 150y