Multiple Choice
Identify the choice that best completes
the statement or answers the question.
____ 1. Microsoft®
Excel, Quattro Pro and Lotus 1-2-3 contain built-in optimizers called
a.
what-if engines.
b.
calculators.
c.
solvers.
d.
risk analyzers.
____ 2.
In the Solver dialog box simple upper and lower bounds for decision variables
are specified by
a.
referring directly to the decision variable cells.
b.
requiring the addition of the bounds above and below
the variable cells.
c.
resolving the problem with the bounds added.
d.
incorporating the bounds in the objective function.
____ 3. Which
button in the Solver parameters window is used to enter new constraints to a
model?
a.
Guess
b.
Add
c.
Change
d.
Delete
____ 4. Models
which are setup in an intuitively appealing, logical layout tend to be the most
a.
Reliable
b.
Modifiable
c.
Auditable
d.
Organized
____ 5. Numeric
constants should be
a.
embedded in formulas.
b.
placed in individual cells
c.
placed in separate workbooks.
d.
entered manually every time a model is solved.
____ 6. The
Auditing tool in Excel is useful for
a.
verifying the equations in a spreadsheet model.
b.
toggling between absolute and relative cell
referencing.
c.
executing the Excel spreadsheet layout Wizard.
d.
naming cells and cell ranges for easier modifiability.
____ 7. The
Guess button on the Solver Parameters box
a.
returns a heuristic solution to the problem.
b.
returns a guess as to the decision variable cells.
c.
determines the Target cell based on specified decision
variable cells.
d.
always works correctly.
____ 8. What
action is required to make Solver solve a specified problem?
a.
Type go in cell A1.
b.
Click the Solve button in the Solver Parameters dialog
box.
c.
Click the Close button in the Solver Parameters dialog
box.
d.
Click the Guess button in the Solver Parameters dialog
box.
____ 9. Problems
which have only integer solutions are called
a.
discrete programming problems
b.
integer programming problems
c.
discrete programming problems
d.
infeasible programming problems
____ 10. How
many decision variables are there in a transportation problem which has 5
supply points and 4 demand points?
a.
4
b.
5
c.
9
d.
20
____ 11. How
many constraints are there in a transportation problem which has 5 supply
points and 4 demand points? (ignore the non-negativity constraints)
a.
4
b.
5
c.
9
d.
20
____ 12. A
heuristic solution is
a.
used by Solver when the Guess button is used.
b.
guaranteed to produce an optimal solution.
c.
used by Solver if Standard GRG Nonlinear method is
selected.
d.
a rule-of-thumb for making decisions.
____ 13. Which
of the following describes Data Envelopment Analysis (DEA).
a.
DEA finds the most effective company among some set of
companies.
b.
DEA determines if a company is converting inputs to
outputs as effectively as possible.
c.
DEA determines how effective a company converts inputs
to outputs compared to other companies.
d.
DEA compares how effective a company converts inputs to
outputs compared to a benchmark composite of all companies.
Scenario 3-2
The Byte computer company produces two models of computers, Plain and
Fancy. It wants to plan how many computers to produce next month to maximize
profits. Producing these computers requires wiring, assembly and inspection
time. Each computer produces a certain level of profits but faces only a
limited demand. There are also a limited number of wiring, assembly and
inspection hours available in each month. The data for this problem is
summarized in the following table.
Computer
Model
Profit per
Model ($)
Maximum
demand
for product
Wiring
Hours
Required
Assembly
Hours
Required
Inspection
Hours
Required
Plain
30
80
.4
.5
.2
Fancy
40
90
.5
.4
.3
Hours
Available
50
50
22
Let
X1 = Number of Plain to produce
X2 = Number of Fancy to produce
MAX:
30 X1 + 40 X2
Subject to:
.4 X1 + .5 X2? 50 (wiring
hours)
.5 X1 + .4 X2? 50 (assembly
hours)
.2 X1 + .2 X2? 22 (inspection
hours)
X1? 80 (Plain computers demand)
X2? 90 (Fancy computers demand)
X1, X2? 0
A
B
C
D
E
1
Byte Computer Company
2
3
Plain
Fancy
4
Number to make:
Total Profit:
5
Unit profit:
30
40
6
7
Constraints:
Used
Available
8
Wiring
0.4
0.5
50
9
Assembly
0.5
0.4
50
10
Inspection
0.2
0.3
22
11
Plain Demand
1
80
12
Fancy Demand
1
90
____ 14. Refer
to Scenario 3-2. What formula should be entered in cell E5 in the accompanying
Excel spreadsheet to compute total profit?
a.
=B4*C4+B5*C5
b.
=SUMPRODUCT(B4:C4,B5:C5)
c.
=SUM(B5:C5)
d.
=SUM(E8:E10)
____ 15. Refer
to Scenario 3-2. Which cells should be changing cells in this problem?
a.
B4:C4
b.
E5
c.
D8:D10
d.
E8:E10
____ 16. Refer
to Scenario 3-2. Which cells should be the constraint cells in this problem?
a.
B4:C4
b.
E5
c.
D8:D12
d.
E8:E12
Scenario 3-4
A financial planner wants to design a portfolio of investments for a
client. The client has $300,000 to invest and the planner has identified four
investment options for the money. The following requirements have been placed
on the planner. No more than 25% of the money in any one investment, at least
one third should be invested in long-term bonds which mature in seven or more
years, and no more than 25% of the total money should be invested in C or D
since they are riskier investments. The planner has developed the following LP
model based on the data in this table and the requirements of the client. The
objective is to maximize the total return of the portfolio.
Investment
Return
Years to Maturity
Rating
A
6.45%
9
1-Excellent
B
7.10%
8
2-Very Good
C
8.20%
5
4-Fair
D
9.00%
8
3-Good
Let
X1 = Dollars invested in A
X2 = Dollars invested in B
X3 = Dollars invested in C
X4 = Dollars invested in D
MAX:
.0645 X1 + .071 X2 + .082 X3
+ .09 X4
Subject to:
X1 + X2 + X3 + X4
? 300000
X1? 75000
X2? 75000
X3? 75000
X4? 75000
X1 + X2 + X4? 100000
X3 + X4? 75000
X1, X2, X3, X4
? 0
A
B
C
D
E
F
G
H
1
Amount
Maximum
Years to
7+ years?
Good or
worse?
2
Bond
Invested
25.0%
Return
Maturity
(1-yes, 0-no)
Rating
(1-yes, 0-no)
3
A
$0
$75,000
6.45%
9
1
1-Excellent
0
4
B
$0
$75,000
7.10%
8
1
2-Very Good
0
5
C
$0
$75,000
8.20%
5
0
4-Fair
1
6
D
$0
$75,000
9.00%
8
1
3-Good
1
7
Total
Invested:
$0
Total:
$0
Total:
$0
Total:
$0
8
Total
Available:
$300,000
Required:
$100,000
Allowed:
$75,000
____ 17. Refer
to Scenario 3-4. Which cells are changing cells in the accompanying Excel
spreadsheet?
a.
B3:B6
b.
B7:I7
c.
C7
d.
E7
Scenario 3-5
A company is planning production for the next 4 quarters. They want to
minimize the cost of production. The production cost is stable but demand and
production capacity vary from quarter to quarter. The maximum amount of
inventory which can be held is 12,000 units and management wants to keep at
least 3,000 units on hand. Quarterly inventory holding cost is 3% of the cost
of production. The company estimates the number of units carried in inventory
each month by averaging the beginning and ending inventory for each month.
There are currently 5,000 units in inventory. The company wants to produce at
no less than one half of its maximum capacity in any quarter.
Quarter
1
2
3
4
Unit Production Cost
$ 300
$ 300
$ 300
$ 300
Units Demanded
2,000
9,000
12,000
11,000
Maximum Production
8,000
7,000
8,000
9,000
Let
Pi = number of units produced in quarter i,
i=1, …, 4
Bi = beginning inventory for quarter i
MIN:
300 P1 + 300 P2 + 300 P3
+ 300 P4 +
9(B1 + B2)/2 + 9(B2 +
B3)/2 + 9(B3 + B4)/2 + 9(B4 + B5)/2
Subject to:
4000? P1? 8000
3500? P2? 7000
4000? P3? 8000
4500? P4? 9000
3000? B1 + P1 – 2000? 12000
3000? B2 + P2 – 9000? 12000
3000? B3 + P3 – 12000? 12000
3000? B4 + P4 – 11000? 12000
B2 = B1 + P1 – 2000
B3 = B2 + P2 – 9000
B4 = B3 + P3 – 12000
B 5 = B4 + P4 – 11000
Pi, Bi? 0
A
B
C
D
E
F
1
Quarter
2
1
2
3
4
3
Beginning Inventory
5,000
11,000
9,000
5,000
4
Units Produced
8,000
7,000
8,000
9,000
5
Units Demanded
2,000
9,000
12,000
11,000
6
Ending Inventory
11,000
9,000
5,000
3,000
7
8
Minimum Production
4,000
3,500
4,000
4,500
9
Maximum Production
8,000
7,000
8,000
9,000
10
11
Minimum Inventory
3,000
3,000
3,000
3,000
12
Maximum Inventory
12,000
12,000
12,000
12,000
13
14
Unit Production Cost
$300
$300
$300
$300
15
Unit Carrying Cost
3.0%
$9.00
$9.00
$9.00
$9.00
16
17
Monthly Production Cost
$2,400,000
$2,100,000
$2,400,000
$2,700,000
18
Monthly Carrying Cost
$72,000
$90,000
$63,000
$36,000
19
20
Total Cost
$9,861,000
____ 18. Refer
to Scenario 3-5. What formula should be entered in cell C6 in the accompanying
Excel spreadsheet to compute ending inventory?
a.
=C3-C4+C5
b.
=C3+C4-C5
c.
=C3-(C4-C5)
d.
=C5-C4-C3
____ 19. Refer
to Scenario 3-5. What formula should be entered in cell C18 in the accompanying
Excel spreadsheet to compute the monthly carrying costs?
a.
=C15*C3+C6
b.
=C15*(C3+C6)
c.
=C15*C3/2
d.
=C15*(C3+C6)/2
____ 20. Refer
to Scenario 3-5. Which cells are changing cells in the accompanying Excel
spreadsheet?
a.
C4:F4
b.
C9:F9
c.
F20
d.
C12:F12
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