BRIEF CALC SEM 1 REVIEW CH 1 Formulas

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: � Point-slope: y = mx + b y – y 1=m(x – x 1) � 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 6 x – 2 y = -5 containing the point (-1, -2) 2. Write an equation in general form parallel to the line x – 2 y = -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 + 3 y = -7 2. x + 2 y = 28 6 x + 40 R = 30 x P = 24 x - 40 3. C =

CHAPTER 2 1. solve using any method 3 x +3 y +2 z = 4 x – 3 y +z = 10 5 x – 2 y – 3 z = 8 2. Determine the number of solutions (one, none or infinite). x–y–z=1 2 x +3 y +z = 2 3 x + 2 y = 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 ]

BRIEF- CALC REVIEW CH 3 1. Determine which region in the graph to the right represents the equations 2 x – 5 y < -5 a and 3 x + 5 y < 30 2. What point would maximize the objective function z = 5 x + 7 y subject to: x + y >2 2 x + y < 10 x > 0 b x+ y < 8 y>0 c d 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 60 x + 30 y < 1800 3 x + 4 y < 120 P = 300 x + 150 y