# 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 = (30000-29000)*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 => 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

- 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 – 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

- Y = 2x -1 (1)

- 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)