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Quantitative Analysis For Business (CBEB1110)|
Group Assignment:|
|
Presented by: (Group 5)
|
Name| Matric No.|
Osama Khalid| CEB120702|
Bill | CEB120|
Hui Dong| CEB120|
| CEB120|
| CEB120|
|
Presented to: Dr. Azmin Azliza Binti AzizFaculty of Business and Accountancy | |
|

Table of Contents
No| Questions and chapter| |
1| Apply it 19 - Chapter 3| |
2| Apply it 16 - Chapter 4| |
3| Apply it 10 - Chapter 10| |
4| Apply it 3 - Chapter 11| |
5| Apply it 5 - Chapter 12| |
6| Problems 17.7.11 - Chapter 17| |

Chapter 3
Apply it 19. A coffee shop specialises in blending gourmet coffees. From type A, type B, and type C coffees, the owner wants to prepare a blend that will sell for $8.50 for a 1-pound bag. The cost per pound of these coffees is $12, $9, and $7, respectively. The amount of type B is to be twice the amount of type A. How much of each type of coffee will be in the final blend? Answer :

We know that: A+B+C=1
B=2A
1 =3A+C
A=(1-C)3
From the question:
12A+9B+7C=8.50
Putting 2A in place of B:
12A+18A+7C=8.50 30A+7C=8.50 30(1-C)3+ 7C=8.50
10-10C+7C=8.50
Therefore, C=0.5
3A+C=1 Substitute in 3A+C=1 3A+ 0.5=1
Therefore, A=16
B=2A Substitute in (1) B=216= 13

Chapter 4
Apply it 16. Greg took a number and multiplied it by a power of 32. Jean started with the same number and got the same result when she multiplied it by 4 raised to a number that was nine less than three times the exponent that Greg used. What power of 32 did Greg use ? Answer :

Let the number slected by boht be 1
let the power of 32 be y
So: 32^y=4^(3y-9)
2^(5y)=2^(6y-18)
5y(log2)=(6y-18)(log2)
6Y-5Y=18
Y=18

Chapter 10
Apply it 10. An open box is formed by cutting a square piece out of each corner of an 8-inch-by-10-inch piece of metal. If each side of the cut-out squares is x inches long, the volume of the box is given by VX= X8 – 2X10 – 2X. This problem makes sense only when this volume is positive. Find the values of x for which the volume is positive. Answer:

VX= X8 – 2X10 – 2X≥0
The roots of the above equation are 0, 4 and 4. To find the values, we would construct the sign chart ∞

∞-
∞-
5
5
4
4
0
0

x
x
-| +| +| +|
+| +| -| -|
10-2x
10-2x
+
+
| +| +| -|
-
-
V(x)
V(x)
| +| -| +|

8-2x
8-2x

From the chart, noting the endpoints required, X8 – 2X10 – 2X ≥0 on [0, 4] ∪ [ 5, ∞)

Chapter 11
Apply it 3. Suppose that the profit P made by selling a certain product at a price of p per unit is given by P = f(p) and the rate of change of that profit with respect to change in price is dPdp= 5 at p = 25. Estimate the change in the profit P if the price changes from 25 to 25.5. Answer:

dP/dp = 5 and ∆p = 25.5-25 = 0.5 .
The change in ∆P, and, from Equation (25),
∆P∆p≈dPdp
∆P=dP/dp(∆p)
∆P=50.5=2.5 units

Chapter 12
Apply it 5. The volume V enclosed by a spherical balloon of radius r is given by the equation v = 43π r3. If the radius is increasing at a rate of 5 inches/minute (that is, drdt=5), then find dVdt when r= 12 , the rate of increase of the volume, when the radius is 12 inches. Answer :

dVdt = dVdr . drdt
dVdr = 3 (43 πr2)
= 4 πr2
drdt = 5
when r=12
dVdt = 4πr2 . 5
= 4π(12)2 . 5
= 9047.79 inches cube per minute.

Chapter 17
Problems 17.7. Find, by the method of Lagrange multipliers, the critical points of the functions, subject to given constraints. 11. fx,y,z= xy2z ; x+y+z = 1, x-y+z = 0 (xyz = 0)
Answer
F(x,y,z)=xy²z; x+y+z=1, x-y+z=0 (xyz≠0)

 For x+y+z=1
Solution: We have
F(x,y,z,λ)=...
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