Transcript Brief Calc * Sem 1 Review Ch 1

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