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SOLUTION AND SENSITIVITY ANALYSIS WITH ANSWERS
RATED A+
- The reduced cost (shadow price) for a positive decision
variable is 0. Answer: TRUE
- When the right-hand sides of 2 constraints are both increased by 1 unit, the value
of the objective function will be adjusted by the sum of the constraints' prices.
Answer: FALSE
- When a linear programming problem is solved using a computer package decision
variables will always be integer and therefore decision variable values never need to be
rounded.
Answer: FALSE
- Sensitivity ranges can be computed only for the right hand sides of
constraints. Answer: FALSE
- Sensitivity analysis determines how a change in a parameter affects the
optimal solution. Answer: TRUE
- The sensitivity range for an objective function coefficient is the range of values over
which the current optimal solution point (product mix) will remain optimal.
Answer: TRUE
- The sensitivity range for an objective function coefficient is the range of values
over which the profit does not change.
Answer: FALSE
- The sensitivity range for a constraint quantity value is the range over which the shadow
price is valid. Answer: TRUE
- If we change the constraint quantity to a value outside the sensitivity range for that
constraint quantity, the shadow price will change.
Answer: TRUE
- The sensitivity range for a constraint quantity value is the range over which the
optimal values of the decision variables do not change.
Answer: FALSE
- Linear programming problems are restricted to decisions in a single time
period. Answer: FALSE
SOLUTION AND SENSITIVITY ANALYSIS WITH ANSWERS
RATED A+
- A maximization problem may be characterized by all greater than or equal
to constraints. Answer: FALSE
- A change in the value of an objective function coefficient will always change the
value of the optimal solution.
Answer: FALSE
- The terms reduced cost, shadow price, and dual price all mean
the same thing. Answer: TRUE
SOLUTION AND SENSITIVITY ANALYSIS WITH ANSWERS
RATED A+
Consider the following linear program, which maximizes profit for two products, regular (R), and super
(S):
MAX 50R + 75S
s.t.
1.2R + 1.6 S ≤ 600 assembly (hours) 0.8R
- 0.5 S ≤ 300 paint (hours)
.16R + 0.4 S ≤ 100 inspection (hours)
SOLUTION AND SENSITIVITY ANALYSIS WITH ANSWERS
RATED A+
Sensitivity Report:
Cell Name
Fina
l
Valu
e
Reduce
d
Cost
Objectiv
e
Coefficie
nt
Allowab
le
Increas
e
Allowab
le
Decreas
e
$B$7 Regular
$C$7 Super = 133.33 0.
Cel
l
Name
Fina
l
Valu
e
Shado
w
Price
Constraint
R.H. Side
Allowab
le
Increas
e
Allowab
le
Decreas
e
$E$
Assembly (hr/unit) 563.33 0.00 600 1E+30 36.
$E$
Paint (hr/unit) 300.00 33.33 300 39.29 175
$E$
Inspect (hr/unit) 100.00 145.83 100 12.94 40
- The optimal number of regular products to produce is
, and the optimal number
SOLUTION AND SENSITIVITY ANALYSIS WITH ANSWERS
RATED A+
Tracksaws, Inc. makes tractors and lawn mowers. The firm makes a profit of $30 on each tractor
and $30 on each lawn mower, and they sell all they can produce. The time requirements in the
machine shop, fabrication, and tractor assembly are given in the table.
Formulation:
Let x = number of tractors produced per period
y = number of lawn mowers produced per period MAX 30x +
30y
subject to 2 x + y ≤ 60
2 x + 3y ≤ 120
x ≤ 45
The graphical solution is shown below.
SOLUTION AND SENSITIVITY ANALYSIS WITH ANSWERS
RATED A+
- How many tractors and saws should be produced to maximize profit, and how
much profit will they make?
Answer: 15 tractors and 30 saws for $1,350 in profit
- Determine the sensitivity range for the profit
for tractors. Answer: 20 ≤ x ≤ 60
- What is the shadow price for assembly?
SOLUTION AND SENSITIVITY ANALYSIS WITH ANSWERS
RATED A+
s.t.
2R + 4D ≤ 480
5R + 3D ≤ 675
The sensitivity report is given below
SOLUTION AND SENSITIVITY ANALYSIS WITH ANSWERS
RATED A+
- What is the optimal daily
profit? Answer: $
- How many cases of regular and how many cases of diet soft drink should Whoppy
produce to maximize daily profit?
Answer: 90 cases of regular and 75 cases of diet
- What is the sensitivity range for the per case profit of a
diet soft drink? Answer: 1.8 ≤ c 2
- What is the sensitivity range of the production
time? Answer: 270 ≤ b
1
- if the company decides to increase the amount of syrup it uses during production of these
soft drinks to 990 lbs. will the current product mix change? If show what is the impact on
profit? Answer: Yes., Increase in profit = 0.57(990 - 675) = $
SOLUTION AND SENSITIVITY ANALYSIS WITH ANSWERS
RATED A+
Answer: the range is from $250 to infinity
- If the Mallory Furniture is able to increase the profit per
medium shelf to $200, would the company purchase medium
shelves. If so, what would be the new product mix and the total
profit?
Answer: yes, Big = 90, Medium = 100 Z = $47,
The linear programming problem whose output follows is used to determine how many bottles of fire
red nail polish (x 1
), bright red nail polish (x 2
), basil green nail polish(x 3
), and basic pink nail
polish(x 4
) a beauty salon should stock. The objective function measures profit; it is assumed that
every piece stocked will be sold. Constraint 1 measures display space in units, constraint 2 measures
time to set up the display in minutes. Note that green nail polish does not require any time to prepare
its display. Constraints 3 and 4 are marketing restrictions. Constraint 3 indicates that the maximum
demand for fire red and green polish is 25 bottles, while constraint 4 specifies that the minimum
demand for bright red, green and pink nail polish bottles combined is at least 50 bottles.
MAX 100x 1
2
3
4
Subject to 1. x 1
3x
1
2
4
- x 1
- x 2
50 x 1
x 2
, x 3
, x 4 ≥
Optimal Solution:
Objective Function Value = 7475.
SOLUTION AND SENSITIVITY ANALYSIS WITH ANSWERS
RATED A+
SOLUTION AND SENSITIVITY ANALYSIS WITH ANSWERS
RATED A+
- a)By how much can the amount of space decrease before there is a change in the profit?
b) By how much can the amount of space decrease before there is a change in the product mix?
c) By how much can the amount of time available to setup the display can increase
before the solution (product mix) would change?
d) What is the lowest value for the amount of time available to setup the display
before the solution (product mix) would change?
Answer: a) 0 b) 8 c) 0 d) 57
SOLUTION AND SENSITIVITY ANALYSIS WITH ANSWERS
RATED A+
- You are offered the chance to obtain more space. The offer is for 15 units and the
total price is $1500. What should you do? Why?
Answer: reject the offer, (11 x 15) = 1125 < 1500
- Max Z = 5x 1
Subject to: 6x 1
15x 1
x 1
Determine the sensitivity range for each constraint.
Answer: constraint 1: 6 - 24
constraint 2:45 - 180
- Max Z = 5x 1
Subject to: 6x 1
2 ≤
15x1 + 20x ≤
x 1
Determine the sensitivity range for each objective function coefficient.
Answer:
x 1
: 2.25 - 9.0 and, x 2
- Max Z = 3x 1
Subject to: 10x 1
25x 1
x 1
, x 2
Determine the sensitivity range for each objective function coefficient.
Answer:
SOLUTION AND SENSITIVITY ANALYSIS WITH ANSWERS
RATED A+
A) the same product mix, different total profit
B) a different product mix, same total profit as before
C) the same product mix, same total profit
D) a different product mix, different
total profit Answer: D
The production manager for Beer etc. produces 2 kinds of beer: light (L) and dark (D). Two
resources used to produce beer are malt and wheat. He can obtain at most 4800 oz of malt per week
and at most 3200 oz of wheat per week respectively. Each bottle of light beer requires 12 oz of malt
and 4 oz of wheat, while a bottle of dark beer uses 8 oz of malt and 8 oz of wheat. Profits for light
beer are $2 per bottle, and profits for dark beer are $1 per bottle.
- If the production manager decides to produce of 0 bottles of light beer and 400
bottles of dark beer, it will result in slack of
A) malt only
B) wheat only
C) both malt and wheat
D) neither malt nor
wheat Answer: A
- Which of the following is not a feasible solution?
A) 0 L and 0 D
B) 0 L and 400 D
C) 200 L and 300 D
D) 400 L and
400 D Answer:
D
What is the optimal weekly profit?
A) $1000 B) $900 C) $800 D) $700 E) $
SOLUTION AND SENSITIVITY ANALYSIS WITH ANSWERS
RATED A+
Answer: C
Mallory Furniture buys 2 products for resale: big shelves (B) and medium shelves (M). Each big shelf
costs $500 and requires 100 cubic feet of storage space, and each medium shelf costs $300 and
requires 90 cubic feet of storage space. The company has $75000 to invest in shelves this week, and
the warehouse has 18000 cubic feet available for storage. Profit for each big shelf is
$300 and for each medium shelf is $150.
- Which of the following is not a feasible purchase combination?
A) 0 big shelves and 200 medium shelves
B) 0 big shelves and 0 medium shelves
C) 150 big shelves and 0 medium shelves
