The Costs of a Large-Scale Machine

Practical Question 1 1 Question 2 1 Question 3 1 Question 4 1 Question 5 2 Question 6 2 Question 7 2 QUESTION 8 2 QUESTION 9 3 Question 10 4 Question 115 QUESTION 12 5 QUESTION 13 6 QUESTION 146 QUESTION 15 7 QUESTION 167 1 Question 1 The company monthly costs are $50 per unit (x), plus $1000 in overhead. 6 Question 6 A) x2* X0 = X2 b) a3b2a

Practical Question

Table of Contents
Question 1....................................................................................................................................1
Question 2....................................................................................................................................1
Question 3....................................................................................................................................1
Question 4....................................................................................................................................1
Question 5....................................................................................................................................2
Question 6....................................................................................................................................2
Question 7....................................................................................................................................2
QUESTION 8...............................................................................................................................2
QUESTION 9 ..............................................................................................................................3
Question 10..................................................................................................................................4
Question 11 .................................................................................................................................5
QUESTION 12.............................................................................................................................5
QUESTION 13.............................................................................................................................6
QUESTION 14 ............................................................................................................................6
QUESTION 15.............................................................................................................................7
QUESTION 16 ............................................................................................................................7

Question 1
The company monthly costs are $50 per unit (x), plus $1000 in overhead. The cost must
be more than 0 and less than $60,000. So, the inequality is as follows :-
0 < 50x + 1000 < 60,000
0 < 50x [phone] < 60,000 -1000
0 < 50x < 59000
0 < 50x < 59000
50 50
0 < x < 1180
Thus, company must produce goods in interval of 1180.
Question 2
The company revenue is 30 per unit (x). Its costs are 10 per unit (x) plus $400 overhead. So, the
inequality is :-
30x > 10x + 400
30x - 10x > 10x- 10x + 400
20x > 400
20x > 400
20 20
X > 20
Thus, company should produce more than 20 units to make profits.
Question 3
B and D are functional graphs.
Question 4
a) Quantity demanded at price $25 is 37.7
b) Domain of function is (0, 50)
c) Range of function is (0, 100)
1

Question 5
A.
f1(x) = -2x + 30
Number of DVD = 10 = x
So number of CD's produced = -2*10 +30 = 10
B.
f2(x) = -1.5x +30
f2(x= 10) = 15
C.
When 10 DVD's are produced
Slope of f1(x) = -2
Slope of f2(x) = -1.5
Thus, f1(x) is more stepper.
Question 6
A) x^2* X^0 = X^2
b) a^3b^2a^5b = a^8b^3
c) x^1/5y^6/5 = xy^6
z^2/5 z^2
d) ln e^ab + lne^3a= ab+3a
e) e^lnx^2= x^2
Question 7
In Y = ln2 + 1 lnK +1 lnL + 1 lnR
2 3 6
QUESTION 8
At maxima and minima point the slope is equals to zero. Thus, for the given function At
point B slope is zero.
2

QUESTION 9
A =
-1 0
3 -2
4 2
5 -3
B =
4 1 2
-1 0 2
C=
1 3 -1 4
-4 2 1 0
AB =
-4 -1 -2
14 3 2
14 4 12
23 5 4
3

CA =
24 -20
14 -2
Question 10
a) A+B=
9
6
b) 4a
8
20
c) -6b
-42
-6
d) 2a – 3b
4

-17
7
Question 11
T h d c
10 15 9 12
20 14 8 5
16 8 15 6
25 15 7 16
5 12 20 18
QUESTION 12
Value of stock prior to the discount = V1 =
5000 4500 6000
10000 12000 7500
8000 9000 11000
V2 =
5000 4500 6000
10000 12000 7500 * 0.8
8000 9000 11000
4000 3600 4800
5

8000 9600 6000
6400 7200 8800
QUESTION 13
A.
y = [ (x^3) + 2 ] / (x – 1)
dy/dx = (x – 1)*{d([ (x^3) + 2 ])/dx} - [ (x^3) + 2 ]*{d(x – 1)/dx}
= { (3x^2) (x – 1) – 1* ([ (x^3) + 2 ]) } / (x – 1)^2
dy/dx = (2x^3 – 3x^2 – 2 ) / [(x -1)^2]
B.
y = e^{(4*x^2) + 3x – 1}
dy / dx = (8x + 3)* (e^{(4*x^2) + 3x – 1})
QUESTION 14
A.
y = (x + 7)*(2x +3)
dy/dx = (2x +3) [d(x +7)/dx] + (x +7) [d(2x +3)/dx]
= 2x + 3 + 2*(x + 7)
dy/dx = 4x +17
B.
y = (x^3 – 2x + 1)^ 15
dy/dx = (2x – 2)*15* [(x^3 – 2x + 1)^ 14 ]
C.
6

y = ln 3x +ln (5 + x^2)
dy /dx = (1/ ln 10) * [d(ln 3x) /dx]
dy/dx = 1/ln x
QUESTION 15
f(x) = 7x^2 – 9x + 3
Slope = dy/dx
dy/dx = 14x – 9
At x = 2
Slope = 19
QUESTION 16
f(x) = - 0.25x^2 + 36
x = coloured printer
f(x) = black and white printer
Rate of instantaneous change = df(x) / dx
df(x) / dx = -0.5x
When number of coloured printers is 10 then rate of change is given by
df(x = 10) / dx = -5
7

1

2