The Costs of a Large-Scale Machine

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