1) A company that manufactures laser printers for computers has monthly fixed costs of $177,000 and variable costs of $650 per unit produced. The company sells the printers for $1,250 per unit. How many printers must be sold each month for the company to break
even?
Hint: Let x represent the number of laser printers. Set up the cost function, and the revenue function. Then set cost function equal to revenue function, and solve for x.
1) _______
A) 195 printers per month
B) 495 printers per month
C) 395 printers per month
D) 295 printers per month
E) none of the above
2) A performance center has 2,500 seats. Tickets for an event are $9 and $12 per seat. Assuming that all tickets are sold and bring in a total of $25,800, how many of each type of ticket were sold? Set up a system of equations, and solve by augmented matrix methods.
Hint: Please see example 1 in section 4.2
2) _______
A) 2,400 $9 seats and 1,500 $12 seats
B) 1,400 $9 seats and 1,100 $12 seats
C) 1,700 $9 seats and 2,100 $12 seats
D) 3,400 $9 seats and 2,600 $12 seats
E) None of the above
3) If $9,000 is to be invested, part at 13% and the rest at 8%, how much should be invested at each rate so that the total annual return will be $810? Set up a system of linear equations, letting x1 represent the amount invested at 13% and x2 the amount invested at
8%. DO NOT SOLVE THE system.
Hint: Please see examples in section 4.2. Also, note 13% = 0.13, and 8% = 0.08
3) _________
A) 0.13X1+ 0.08X2= 9,000
X1 + X2 = 810
B) X1 + X2 = 9,000
0.13X1+ 0.08X2= 810
C) X1 + X2 = 810
0.013X1 + 0.54X2= 9000
D) X1 + X2 = 900
0.12X1+ 0.07X2= 9800
E) None of the above
4) Labor and material costs for manufacturing each of three types of products, M, N, and P, are given in the table:
PRODUCT
M N P
LABOR $50 $40 $50
MATERIALS $60 $40 $70
The weekly allocation for labor is $50,000 and for materials is $80,000. There are to be 3 times as many units of product M manufactured as units of product P. How many of each type of product would be manufactured each week to use exactly each of the weekly allocations? Set up a system of linear equations, letting X1, X2, and X3 represent the number of units of products M, N, and P, respectively, manufactured in one week. DO NOT SOLVE THE SYSTEM. Hint: Please see examples in section 4.2.
4) _________
A) 50X1 + 40X2 + 50X3 = 80,000
50X1 + 20X2 + 70X3 = 55,000
3X1 - X3 = 0
B) 75X1 + 35X2 + 50X3 = 80,000
40X1 + 40X2 + 70X3 = 50,000
X1 - 2X3 = 0
C) 50X1 + 40X2 + 50X3 = 50,000
60X1 + 40X2 + 70X3 = 80,000
X1 - 3X3 = 0
D) 50X1 + 40X2 + 50X3 = 95,000
20X1 + 30X2 + 80X3 = 80,000
2X1 - 2X3 = 0
E) None of the above
5) Solve the following by augmented matrix methods:
5) _______
-7X1 + 6X2 = -5
X1 - X2 = -5
Hint: Please see example 1 in section 4.2
A) X1 = 35 AND X2 = 40
B) X1 = 37 AND X2 = 25
C) X1 = 38 AND X2 = 49
D) X1 = 40 AND X2 = 35
E) None of the above
6) Solve the following
-3 4 25
1 -2 -11
? ? ? ? ? ?
by augmented matrix methods
Hint: Please see example 1 in section 4.2 6) _______
A) x = -9 AND y =9
B) x = -8 AND y =5
C) x = 3 AND y = -4
D) x = -3 AND y =4
E) None of the above
7) Solve by augmented matrix methods:
3X1 - X2 = -5
X1 + 3 X2 = 5 7) _______
Hint: Please see example 2 in section 4.2
A) X1 = 2; X2 = -5
B) X1 = -2; X2 = -3
C) X1 = -1; X2 = -5
D) X1 = -1; X2 = 2
E) None of the above
8) A hospital dietitian wants to insure that a certain meal consisting of rice, broccoli, and fish contains exactly 26,800 units of vitamin A, 840 units of vitamin E, and 11,160 units of vitamin C. One ounce of rice contains 400 units of vitamin A, 20 units of vitamin E, and
180 units of vitamin C. One ounce of broccoli contains 800 units of vitamin A, 60 units of vitamin E, and 540 units of vitamin C. One ounce of fish contains 2,400 units of vitamin A, 40 units of vitamin E, and 810 units of vitamin C. Set up a system of linear equations,
letting X1, X2, and X3 represent the number of ounces of rice, broccoli, and fish, respectively, of which should this meal include. DO NOT SOLVE THE SYSTEM.
Hint: Please see examples in section 4.2. 8) _______
A) 2 ounces rice, 9 ounces broccoli, 5 ounces fish
B) 3 ounces rice, 8 ounces broccoli, 9 ounces fish
C) 7 ounces rice, 5 ounces broccoli, 3 ounces fish
D) 12 ounces rice, 9 ounces broccoli, 10 ounces fish
E) None of the above
9) Find the coordinates of the corner points of the solution region for:
3X + 2Y
?
54
4X + 5Y
?
100
X
? 0
Y
? 0
Hint: Please see example 2 in section 5.2. 9) _______
A) (0,18), (21,25), (12,10)
B) (18,0), (25,0), (10,12)
C) (11,10), (21,0), (14,11)
D) (11,9), (22,10), (11,15)
E) None of the above
10) Given the following system of inequalities
5X1 + 2X2
?
40
X1 + 3X2
?
21
X1
? 0
X2
? 0
The corner points for the bounded feasible region determined by the system of inequalities are O = (0,0), A = (0,7), B = (6,5) and C = (8,0). Find the optimal solution for the objective profit function: P = 5X1 + 5X2.
Hint: Please see example 2 in section 5.2. 10) ______
A) Maximum occurs at (5, 6) and is 75.
B) Maximum occurs at (6, 6) and is 50.
C) Maximum occurs at (7, 7) and is 49.
D) Maximum occurs at (6, 5) and is 55.
E) None of the above