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 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.

 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
 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.

 If you earn$ 30000 per year and spend $29000 per year, write and equation for the amount you save after y years, if you start with nothing.
 X = (3000029000)*y
 X = 1000y
 If you earn$ 30000 per year and spend $29000 per year, write and equation for the amount you save after y years, if you start with nothing.
 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 => 4X6Y =0 eq(2)
 Multiply eq(1) with 6 => 6X +6Y = 27000 eq(3) Add eq(2) and eq(3)
 10X27000 => X=2700 So, Y = 45002700 = 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= 3y4000 x+y=24000
 x3y=4000 (* 1) 4y=28000
 y= 7000
 x= 3*7000 â€“ 4000 x = 17000
 Kim invested $7000 in the equity fund and $17000 in the Bond value.
 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.

 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 = Andreaâ€™s sales X + y = 940
 X = 3y 140 X + y = 940
 X â€“ 3y = 140 (* 1) 4y = 1080
 Y = 270
 X+270 = 940
 X = 670
 Nancy sold $670 and Andrea sold $270.
 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?
 Solve the system of equations: 2x + 6y = 12Â Â 2x – 5y = 10
 2x + 6y = 12
 2x – 5y = 10 (* 1)
 11y = 22
 Y = 2
 2x + 6*(2) = 12
 2x â€“ 12 = 12
 2x = 0
 X = 0
 Find the slope and yintercept: (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 yintercept: 0.22
 Y=0.5x+4
 Slope: 0.5 yintercept: 4
 y= 4
 slope: 0 yintercept: 4
 x=12 => 12x =0
 Infinite slope, no y intercept
 4.5x + 9 y = 2 b) x + 2y = 8 c) 4y = 16 d) x = 12
 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 â€“ y = 1
 y = 1 â€“ 2x
 Y = 2x â€“ 1 (1)
 2x + y = 8 Y = 8 â€“ 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
 Y = 2x 1 (1)
 Using X in the equation (1) Y = 2*(2.25) â€“ 1
 Y = 3.5
 Â Intersection between the two lines is A (2.25, 3.5)
