Fundamentals of Numeric Computing

CPAN 112 || Lab 02

Please read the following instruction very carefully before answering any questions:

• Please read all the questions very carefully.
• Please provide your answers in the boxes below each question, and do not change the text colour.
• Your answer MUST show the solution procedure.
• There is no credit if you only state the final answer.
• Please underline your final answer to each question.
• Please keep the naming conventions requested in this lab and each question.
• Once you complete your lab, rename your word document file to the (CPAN112_LabXX_FirstName_LastName). Replace XX with the lab number (e.g. 01). Replace FirstName and LastName with your first name and last name, respectively.

It will be a 10% mark deduction if you do not follow the guidelines mentioned above

 

• Set up an Equation for:
  • A manufacturer makes two type of products profit on Product A is $30 per unit and profit on Product B is $40 per unit. Budgeted monthly profit is $6000.
    • 30x+40y=6000

• • A manufacturer processes two type of products. Each unit of the product A needs 20 time units in finishing while product B needs 30 time units. Per day 1200 time units are available. Set up an equation that describes the relationship between the number of units.
    • 20x+30y=1200

• • If you earn$ 30000 per year and spend $29000 per year, write and equation for the amount you save after y years, if you start with nothing.
    • X = (30000-29000)*y
    • X = 1000y

 

• Setup the equation and solve:
  • Terry invested a total of $4500. A portion was invested at 4% and the rest was invested at 6%. The amount of Terry’s annual return on each portion is the same. Find the average rate of interest Terry earned on his total investment.

• • • Total invested 2 Portions i.e. X+Y = 4500 eq(1)
    • X*4/100=Y*6/100 => 4X-6Y =0 eq(2)
    • Multiply eq(1) with 6 => 6X +6Y = 27000 eq(3) Add eq(2) and eq(3)
    • 10X-27000 => X=2700 So, Y = 4500-2700 = 1800
    • Total Return => 2700*4/100 + 1800*6/100 = 216 Avg Return = 216/4500 *100 = 4.8%

• • Kim invested a total of $ 24000 in two mutual funds. Her investment in the equity fund is $4000 less than three times her investment in the Bond value. How much did Kim invested in each value.
    • X = equity fund Y = Bond value x+y= 24000
    • x= 3y-4000 x+y=24000
    • x-3y=-4000 (* -1) 4y=28000
    • y= 7000
    • x= 3*7000 – 4000 x = 17000
    • Kim invested $7000 in the equity fund and $17000 in the Bond value.

• • Nancy’s sales last week were $140 less than three times Andrea’s sales. Together they sold $940. Determine how much each person sold last week?
    • X = Nancy sales
    • Y = Andrea’s sales X + y = 940
    • X = 3y -140 X + y = 940
    • X – 3y = -140 (* -1) 4y = 1080
    • Y = 270
    • X+270 = 940
    • X = 670
    • Nancy sold $670 and Andrea sold $270.

 

• Solve the system of equations: 2x + 6y = -12   2x – 5y = 10
  • 2x + 6y = -12
  • 2x – 5y = 10 (* -1)
  • 11y = -22
  • Y = -2
  • 2x + 6*(-2) = -12
  • 2x – 12 = -12
  • 2x = 0
  • X = 0

 

• Find the slope and y-intercept: (Rewrite the equation in y = mx +b form)
  • 4.5x + 9 y = 2 b) x + 2y = 8 c) 4y = 16 d) x = 12
    • Y=(-4.5x+2)/9 Y = -0.5x + 0.22
    • Slope: -0.5 y-intercept: 0.22
  • Y=-0.5x+4
    • Slope: -0.5 y-intercept: 4
  • y= 4
    • slope: 0 y-intercept: 4
  • x=12 => 12-x =0
    • Infinite slope, no y intercept

 

• Graph: x + 4y = 8. Rewrite the equation in y = mx +b form Slope m = Rise/ Run =
• Rise = Run =
• 
  • X + 4y = 8 4y = -x + 8
  • Y = -0.25x + 2
  • Slope m = -0.25/1 = -0.25 Rise = – 0.25
  • Run = 1

• x	0	1	2	3	4	5	6	7	8
  y	2	1.75	1.5	1.25	1	0.75	0.5	0.25	0

 

6. Solve graphically: 2x – y = 1 and 2x + y = 8 ( Find the point of intersection, Where the lines cross each other).

• 2x – y = 1
• -y = 1 – 2x
• Y = 2x – 1 (1)
• 2x + y = 8 Y = 8 – 2x
• Y = -2x + 8 (2)

 

7.

x	0	1	2	3	4	5
y	-1	1	3	5	7	9
x	0	1	2	3	4	5
y	8	6	4	2	0	-2

• Using the first equation into the second:
  • • Y = 2x -1 (1)
      • Y = -2x + 8 (2)
      • (1) = (2)
      • 2x -1 = -2x +8
      • 4x = 9
      • X = 9/4 = 2.25
  • Using X in the equation (1) Y = 2*(2.25) – 1
  • Y = 3.5
  •  Intersection between the two lines is A (2.25, 3.5)