UNLV
University of Nevada, Las Vegas
The Department of Mathematical Sciences
Math 132 Special Homework Assignment I
Revised 2.15.2016
While all material covered in the text and listed on the syllabus is essential for success in the
course, the following material is of critical importance in Math 132. Problems included in this
document are a compilation of exam problems from previous semesters, and are similar to the
problems in the class text: Finite Mathematics, an Applied Approach, 10th edition.
1. For the line 3x + 2y = 18 find the slope and the y-intercept.
2. For the line 5x – 3y = 30, find the x-intercept and the y-intercept and shade the points in the solution
set satisfying the inequality 5x – 3y > 30. Is the solution set bounded?
Yes
No
3. Determine if the following pair of lines are (i) intersecting or (ii) parallel and distinct or (iii) parallel
and coincident or (iv) perpendicular. DO NOT GRAPH.
In each case give your reason for your conclusion.
(a) 4x + 3y = 24, 6x – 8y = 32.
(b) 2x – 5y = 10, 6x – 15y = 45
(c) 4x + 5y = 10, 5x + 4y = 12.
(d) 3x – 5y = 10, -9x + 15y = -30.
4. Find the point of intersection of the pair of lines: 3x + 5y =12, 5x +3y = 4.
5. Find the equation of the line in General (Standard) form through the point (-2,-3) and (i)
perpendicular to 3x + 5y = 15, (ii) parallel to 5x + 7y = 35.
6. Find the Market Price for the following pair of Supply and Demand equations: S = 35p + 700, D =
1150 – 10p, where p is in dollars.
7. A toy manufacturing company sells all the toys it produces at $15 per toy. The company’s monthly
overhead cost is $65,000 and the material cost of production is $5 per toy. Find the breakeven point
8. By graphing, find the minimum and maximum of the objective function
Q = 5x + 7y
subject to the following constraints: 2x + y > 18, x + 2y > 18,
2x + y < 36, x + 2y < 36, x >
0, y > 0.
9. An automobile manufacturing company produces only two lines of cars – sedans, and racecars. For
each sedan, the mechanics take 8 hours to assemble the body and the parts together, the painters and
finishers take 6 hours to paint and finish. Each racecar takes 16 hours for assembly, and 6 hours for
painting and finishing. The team of mechanics can work no more than 256 hours per week, and the
painters and finishers can work utmost 120 hours per week. The company sells each sedan at a profit
of $300, and each racecar brings in a profit of $400. By graphing, find the maximum weekly profit
for the company and the corresponding production schedule.
10. If possible, solve for x and y given that
 x 4 y - x
 y 2 1   x + 2 8 2y 
2 
-3 x



5 

 x 1 2   -1 2x + 1 9 
11. Multiply the following given matrices:
2
(a) 
4
6
(b) 7

8
-3
5 
7
 1 6
-3 2  =


8  -7 5 1 
8 9   5 -2 -2 =
9 11  1 -2 1 
Are the matrices in (b) inverse of each other?
Yes.___ No.___
12. Find A 1 for the following given matrices:
3 2 
(a) A = 

4 2
3 4 5 
(b) A =  4 5 6


5 6 8 
 2 3 4
-5 5 -1
13. Given that the matrices 3 4 5  and  5 -6 2 are inverses of each other, by using the




 4 5 5
-1 2 -1
appropriate inverse, solve the following system of equations:
(a) 2x + 3y + 4z = 12
(b) -5x + 5y – z = 3
3x + 4y + 5z = 16
5x  6y +2z = -2
4x + 5y + 5z = 19
-x + 2y – z = 1
14. Using the elementary row operations on the Augmented Matrix of the system and reducing it to the
Reduced Row-echelon form, determine if the following systems of equations are (i) inconsistent
having no solution, or (ii) consistent and independent having unique solution, or (iii) consistent and
dependent having many or infinitely many solutions. In case the system admits many or infinitely
many solutions, give a general solution. For part (c), also solve by using inverse.
(a) x + 2y + 3z = 3
(b) 2x + 3y + 4z = 5
(c) 3x + 4y + 5z = 4
2x + 3y + 4z = 6
3x + 4y + 5z = 6
4x + 5y + 6z = 5
3x + 4y + 5z = 5
4x + 5y + 6z = 7
5x + 6y + 8z = 7
15. A fast-food drive-in-counter serves only three kinds of sandwiches. A deluxe hamburger at $4 each,
a grilled chicken sandwich at $5 each, and a vegetarian super grilled cheese at $3 each. Terry bought
exactly 15 sandwiches for 15 people in the picknic group and paid exactly $57. Find a general
solution for the possible number of sandwiches of each kind that can be bought, and list three
positive integral solutions.
16. Maximize the object function P=60x 1 +48x 2 +42x 3 , subject to x 1  0,x 2  0,x 3  0, and the linear
constraints x1 +2x 2 +x 3  72, 2x1 +x 2 +x 3  66, 3x1 +x 2 +2x 3  102 . Write the maximum value of P
and the corresponding values of x 1 , x 2 , and x 3 that maximizes P.
17. Minimize the objective function C=60x 1 +48x 2 +42x 3 subject to x 1  0,x 2  0,x 3  0, and the linear
constraints x 1 +2x 2 +x 3  72, 2x 1 +x 2 +x 3  66, 3x 1 +x 2 +2x 3  102. Write the minimum value of C
and the corresponding values of x 1 ,x 2 , and x 3 that minimizes C. Also give the answer for the
corresponding Dual Maximization Problem
18. Minimize the objective function C=8x 1 +9x 2 +10x 3 subject to x 1  0,x 2  0,x 3  0, and the linear
constraints 2x 1 +3x 2 +5x 3  30, x 1 +2x 2 +2x 3  16. Write the minimum value of C and the
corresponding values of x 1 , x 2 , and x 3 that minimizes C. Also give the answer for the
corresponding Dual Maximization Problem.
19. Maximize P = 4x + y + 2z, subject to 3x + y + z < 50, 5x + y + 3z < 110, for non-negative variables
x, y, and z.
20. Minimize C = 4x + y + 2z, subject to 3x + y + z > 50, 5x + y +3z > 110 for non-negative variables x,
y, and z.
Mathematics 132 Special Homework Assignment – I /Answers
1. m =  32 , (0, b=9).
2. (6, 0), (0,-10); No.
3. (a) (i) & (iv), (b) (ii), (c) (i), (d) (iii).
4. (-1,3).
5. (i) 5x – 3y =  1, (ii) 5x + 7y =  31.
6. $10.
7. (6,500 toys/m, $97,500/m)
8. Min Q = 72 at x = 6, y = 6, & Max Q = 144 at x = 12, y = 12.
9. Maximum Weekly Profit = $7,200 when 8 Sedans and 12 Racecars are manufactured and sold.
10. x = 1 and y = 1.
6
 11
11. (a). 
 , (b) I 3 , Yes.
-11 34 
-4 2 1 
-1 1
12. (a) 
, (b)  2 1 -2
3


 2 -2
 1 -2 1
13. (a) x = 1, y = 2, z = 1 and (b) x = 4, y = 6, z = 7.
14. (a) (i) , (b) (iii) x = t – 2, y = 3 – 2t, z = t, where t is any real number, (c) (ii) x = 1, y =  1, z = 1.
-4 2 1 
1
A   2 1 -2 
 1 -2 1 
15. A General solution is x = 18 – 2t, y = t – 3, 3  z  t  9 and for 4<t<8 you have five different
positive integral solutions that can be listed by substituting for t, in the general solution, the integers
t = 4, 5, 6, 7, and 8.
16. Maximum P = 2592, when x 1 = 12, x 2 = 18, x 3 = 24.
17. Minimum C = 2592, when x1  12, x 2  18, x 3  24. For Dual Maximization Problem, Maximum
P=2592, when y1  15, y2  9, y3  9 .
18. Minimum C = 75, when x1  0, x 2  5, x 3  3. For the Dual Maximization Problem, Maximum P =
75, when y1  12 and y2  154 
19. Maximum P = 80, when x  10  12 y, z  20  12 y, 0  y  20 . There are nine positive integral
solutions for the variables x, y, and z.
20. Minimum C = 80, when y  20  2x, z  30  x, 0  x  10. There are nine positive integral solutions
for the variables x, y, and z.