# Project #1912 - Linear Programming

Name:
Class: Linear Programing
Date:

MUST SHOW WORK

Topic:  FOUR SPECIAL CASES IN LP
1) Consider the following linear programming problem:

Maximize        12x + 10y
Subject for      2x+3y ≤ 480
4x + 3y ≤ 360
all variables ≥ 0

The maximum possible value for the objective function is
A) 360.
B) 480.
C) 1520.
D) 1560.
E) None of the above

2) Consider the following linear programming problem:

Maximize        12x + 10y
Subject for      4x+3y ≤ 480
2x + 3y ≤ 360
all variables ≥ 0

Which of the following points (X,Y) is feasible?
A) (10,120)
B) (120,10)
C) (30,100)
D) (60,90)
E) None of the above

3) Consider the following linear programming problem

Maximize        5x + 6y
Subject for      4x+2y ≤ 420
1x + 2y ≤ 120
all variables ≥ 0

4) Consider the following linear programming problem:

Maximize        5x + 6y
Subject for      4x+2y ≤ 420
1x + 2y ≤ 120
all variables ≥ 0

Which of the following points (X,Y) is feasible?
A) (50,40)
B) (30,50)
C) (60,30)
D) (90,20)
E) None of the above

8) Consider the following linear programming problem:

Maximize        10x + 30y
Subject for      x+2y ≤ 80
8x + 16y ≤ 640
4x + 2y ≥ 100
X,Y ≥ 0

This is a special case of a linear programming problem in which
A) there is no feasible solution.
B) there is a redundant constraint.
C) there are multiple optimal solutions.
D) this cannot be solved graphically.
E) None of the above

9) Consider the following constraints from a linear programming problem:

2X + Y ≤ 200
X + 2Y ≤ 200
X, Y ≥ 0

If these are the only constraints, which of the following points (X,Y) cannot be the optimal solution?
A) (0, 0)
B) (0, 100)
C) (65, 65)
D) (100, 0)
E) (66.67, 66.67)

10) A furniture company is producing two types of furniture. Product A requires 8 board feet of wood and 2 lbs of wicker. Product B requires 6 board feet of wood and 6 lbs of wicker. There are 2000 board feet of wood available for product and 1000 lbs of wicker. Product A earns a profit margin of \$30 a unit and Product B earns a profit margin of \$40 a unit. Formulate the problem as a linear program.

11) As a supervisor of a production department, you must decide the daily production totals of a
certain product that has two models, the Deluxe and the Special.  The profit on the Deluxe model is \$12 per unit and the Special's profit is \$10.  Each model goes through two phases in the production process, and there are only 100 hours available daily at the construction stage and only 80 hours available at the finishing and inspection stage.  Each Deluxe model requires 20 minutes of construction time and 10 minutes of finishing and inspection time.  Each Special model requires 15 minutes of construction time and 15 minutes of finishing and inspection time.  The company has also decided that the Special model must comprise at least 40 percent of the production total.

____________

Table 8-2
A small furniture manufacturer produces tables and chairs.  Each product must go through three stages of the manufacturing process: assembly, finishing, and inspection.  Each table requires 4 hours of assembly, 3 hours of finishing, and 1 hour of inspection.  Each chair requires 3 hours of assembly, 2 hours of finishing, and 2 hours of inspection.  The selling price per table is \$140 while the selling price per chair is \$90.  Currently, each week there are 220 hours of assembly time available, 160 hours of finishing time, and 45 hours of inspection time.  Assume that one hour of assembly time costs \$5.00; one hour of finishing time costs \$6.00; one hour of inspection time costs \$4.50; and that whatever labor hours are not required for the table and chairs can be applied to another product.  Linear programming is to be used to develop a production schedule.  Define the variables as follows:

1) According to Table 8-2, which describes a production problem, suppose you realize that you can trade off assembly hours for finishing hours, but that the total number of finishing hours, including the trade-off hours, cannot exceed 240 hours.  How would this constraint be written?
A) 7T + 5C ≤ 360
B) 3T + 2C ≤ 240
C) 4T + 3C ≤ 140
D) −T − C ≤ 80
E) None of the above

2) Suppose that the problem described in Table 8-2 is modified to specify that one-third of the tables produced must have 6 chairs, one-third must have 4 chairs, and one-third must have 2 chairs.  How would this constraint be written?
A) C = 4T
B) C = 2T
C) C = 3T
D) C = 6T
E) None of the above

Table 8-5
Ivana Myrocle wishes to invest her inheritance of \$200,000 so that her return on investment is
maximized, but she also wishes to keep her risk level relatively low.  She has decided to invest hermoney in any of three possible ways: CDs, which pay a guaranteed 6 percent; stocks, which have an  expected return of 13 percent; and a money market mutual fund, which is expected to return 8 percent.  She has decided that any or all of the \$200,000 may be invested, but any part (or all) of it may be put in any of the 3 alternatives.  Thus, she may have some money invested in all three alternatives.  In formulating this as a linear programming problem, define the variables as follows:

3) According to Table 8-5, which describes an investment problem, suppose that Ivana has decided that the amount invested in stocks cannot exceed one-fourth of the total amount invested.  Which is the best way to write this constraint?
A) S ≤ 100,000/4
B) 0.13S ≤ 0.24C + 0.32M
C) -C + 4S - M ≤ 0
D) S ≤ (C + M) / 4
E) -C + 3S - M ≤ 0

4) According to Table 8-5, which describes an investment problem, suppose that Ivana has assigned
the following risk factors to each investment instrument  CDs (C): 1.2; stocks (S): 4.8; money
market mutual fund (M): 3.2.  If Ivana decides that she wants the risk factor for the whole investment
to be less than 3.3, how should the necessary constraint be written?
A) 1.2C + 4.8S + 3.2M ≤ 3.3
B) C + S + M ≤ 3.3
C) 1.2C + 4.8S + 3.2M ≤ 3.3(C + S + M)
D) (1.2C + 4.8S + 3.2M)/3 ≤ 3.3
E) S = 0

5) According to Table 8-5, which describes an investment problem, suppose that Ivana has decided that the amount invested in stocks cannot exceed one-fourth of the total amount invested.  Which is the best way to write this constraint?
A) S ≤ 100,000/4
B) 0.13S ≤ 0.24C + 0.32M
C) -C + 4S - M ≤ 0
D) S ≤ (C + M) / 4
E) -C + 3S - M ≤ 0

 Subject Mathematics Due By (Pacific Time) 01/23/2013 12:00 am
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