Question 1
A heuristic solution is
Question 2
How many decision variables are there in a transportation problem which has 5 supply points and 4 demand points?
Question 3
The following questions are based on this problem and accompanying Excel windows.
Jones Furniture Company produces beds and desks for college students. The production process requires carpentry and varnishing. Each bed requires 6 hours of carpentry and 4 hour of varnishing. Each desk requires 4 hours of carpentry and 8 hours of varnishing. There are 36 hours of carpentry time and 40 hours of varnishing time available. Beds generate $30 of profit and desks generate $40 of profit. Demand for desks is limited, so at most 8 will be produced.
Let X1 = Number of Beds to produce
X2 = Number of Desks to produce
The LP model for the problem is
|
MAX:
|
30 X1 + 40 X2
|
|
Subject to:
|
6 X1 + 4 X2£ 36 (carpentry)
|
|
|
4 X1 + 8 X2£ 40 (varnishing)
|
|
|
X2£ 8 (demand for desks)
|
|
|
X1, X2³ 0
|
|
|
A
|
B
|
C
|
D
|
E
|
|
1
|
|
Jones Furniture
|
|
|
|
2
|
|
|
|
|
|
|
3
|
|
Beds
|
Desks
|
|
|
|
4
|
Number to make:
|
|
|
|
Total Profit:
|
|
5
|
Unit profit:
|
30
|
40
|
|
|
|
6
|
|
|
|
|
|
|
7
|
Constraints:
|
|
|
Used
|
Available
|
|
8
|
Carpentry
|
6
|
4
|
|
36
|
|
9
|
Varnishing
|
4
|
8
|
|
40
|
|
10
|
Desk demand
|
|
1
|
|
8
|
| |
|
|
|
|
|
Refer to Exhibit 3.1. Which cells should be changing cells in this problem?
Question 4
How many constraints are there in a transportation problem which has 5 supply points and 4 demand points? (ignore the non-negativity constraints)
Question 5
The following questions are based on this problem and accompanying Excel windows.
ones Furniture Company produces beds and desks for college students. The production process requires carpentry and varnishing. Each bed requires 6 hours of carpentry and 4 hour of varnishing. Each desk requires 4 hours of carpentry and 8 hours of varnishing. There are 36 hours of carpentry time and 40 hours of varnishing time available. Beds generate $30 of profit and desks generate $40 of profit. Demand for desks is limited, so at most 8 will be produced.
Let X1 = Number of Beds to produce
X2 = Number of Desks to produce
The LP model for the problem is
|
MAX:
|
30 X1 + 40 X2
|
|
Subject to:
|
6 X1 + 4 X2£ 36 (carpentry)
|
|
|
4 X1 + 8 X2£ 40 (varnishing)
|
|
|
X2£ 8 (demand for desks)
|
|
|
X1, X2³ 0
|
| |
|
|
|
A
|
B
|
C
|
D
|
E
|
|
1
|
|
Jones Furniture
|
|
|
|
2
|
|
|
|
|
|
|
3
|
|
Beds
|
Desks
|
|
|
|
4
|
Number to make:
|
|
|
|
Total Profit:
|
|
5
|
Unit profit:
|
30
|
40
|
|
|
|
6
|
|
|
|
|
|
|
7
|
Constraints:
|
|
|
Used
|
Available
|
|
8
|
Carpentry
|
6
|
4
|
|
36
|
|
9
|
Varnishing
|
4
|
8
|
|
40
|
|
10
|
Desk demand
|
|
1
|
|
8
|
| |
|
|
|
|
|
Which cells should be the constraint cells in this problem?
Question 6
The following questions are based on this problem and accompanying Excel windows.The Byte computer company produces two models of computers, Plain and Fancy. It wants to plan how many computers to produce next month to maximize profits. Producing these computers requires wiring, assembly and inspection time. Each computer produces a certain level of profits but faces only a limited demand. There are also a limited number of wiring, assembly and inspection hours available in each month. The data for this problem is summarized in the following table.
|
Computer
Model
|
Profit per
Model ($)
|
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 computers to produce
|
|
|
X2 = Number of Fancy computers 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, X2³ 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
|
| |
|
|
|
|
|
Which cells should be the constraint cells in this problem?
Question 7
Numeric constants should be
Question 8
What is the significance of an absolute cell reference in Excel?
Question 9
An LP problem with a feasible region will have
Question 10
Problems which have only integer solutions are called
Question 11
The following questions are based on this problem and accompanying Excel windows.Jones Furniture Company produces beds and desks for college students. The production process requires carpentry and varnishing. Each bed requires 6 hours of carpentry and 4 hour of varnishing. Each desk requires 4 hours of carpentry and 8 hours of varnishing. There are 36 hours of carpentry time and 40 hours of varnishing time available. Beds generate $30 of profit and desks generate $40 of profit. Demand for desks is limited, so at most 8 will be produced.
|
Let
|
X1 = Number of Beds to produce
|
|
|
X2 = Number of Desks to produce
|
| |
|
The LP model for the problem is
|
MAX:
|
30 X1 + 40 X2
|
|
Subject to:
|
6 X1 + 4 X2£ 36 (carpentry)
|
|
|
4 X1 + 8 X2£ 40 (varnishing)
|
|
|
X2£ 8 (demand for desks)
|
|
|
X1, X2³ 0
|
| |
|
|
|
A
|
B
|
C
|
D
|
E
|
|
1
|
|
Jones Furniture
|
|
|
|
2
|
|
|
|
|
|
|
3
|
|
Beds
|
Desks
|
|
|
|
4
|
Number to make:
|
|
|
|
Total Profit:
|
|
5
|
Unit profit:
|
30
|
40
|
|
|
|
6
|
|
|
|
|
|
|
7
|
Constraints:
|
|
|
Used
|
Available
|
|
8
|
Carpentry
|
6
|
4
|
|
36
|
|
9
|
Varnishing
|
4
|
8
|
|
40
|
|
10
|
Desk demand
|
|
1
|
|
8
|
| |
|
|
|
|
|
What formula should be entered in cell D8 in the accompanying Excel spreadsheet to compute the amount of carpentry used?
Question 12
The following questions are based on this problem and accompanying Excel windows.Jones Furniture Company produces beds and desks for college students. The production process requires carpentry and varnishing. Each bed requires 6 hours of carpentry and 4 hour of varnishing. Each desk requires 4 hours of carpentry and 8 hours of varnishing. There are 36 hours of carpentry time and 40 hours of varnishing time available. Beds generate $30 of profit and desks generate $40 of profit. Demand for desks is limited, so at most 8 will be produced.
|
Let
|
X1 = Number of Beds to produce
|
|
|
X2 = Number of Desks to produce
|
| |
|
The LP model for the problem is
|
MAX:
|
30 X1 + 40 X2
|
|
Subject to:
|
6 X1 + 4 X2£ 36 (carpentry)
|
|
|
4 X1 + 8 X2£ 40 (varnishing)
|
|
|
X2£ 8 (demand for desks)
|
|
|
X1, X2³ 0
|
| |
|
|
|
A
|
B
|
C
|
D
|
E
|
|
1
|
|
Jones Furniture
|
|
|
|
2
|
|
|
|
|
|
|
3
|
|
Beds
|
Desks
|
|
|
|
4
|
Number to make:
|
|
|
|
Total Profit:
|
|
5
|
Unit profit:
|
30
|
40
|
|
|
|
6
|
|
|
|
|
|
|
7
|
Constraints:
|
|
|
Used
|
Available
|
|
8
|
Carpentry
|
6
|
4
|
|
36
|
|
9
|
Varnishing
|
4
|
8
|
|
40
|
|
10
|
Desk demand
|
|
1
|
|
8
|
| |
|
|
|
|
|
What formula should be entered in cell E5 in the accompanying Excel spreadsheet to compute total profit?
Question 13
The following questions are based on this problem and accompanying Excel windows.Jones Furniture Company produces beds and desks for college students. The production process requires carpentry and varnishing. Each bed requires 6 hours of carpentry and 4 hour of varnishing. Each desk requires 4 hours of carpentry and 8 hours of varnishing. There are 36 hours of carpentry time and 40 hours of varnishing time available. Beds generate $30 of profit and desks generate $40 of profit. Demand for desks is limited, so at most 8 will be produced.
|
Let
|
X1 = Number of Beds to produce
|
|
|
X2 = Number of Desks to produce
|
| |
|
The LP model for the problem is
|
MAX:
|
30 X1 + 40 X2
|
|
Subject to:
|
6 X1 + 4 X2£ 36 (carpentry)
|
|
|
4 X1 + 8 X2£ 40 (varnishing)
|
|
|
X2£ 8 (demand for desks)
|
|
|
X1, X2³ 0
|
| |
|
|
|
A
|
B
|
C
|
D
|
E
|
|
1
|
|
Jones Furniture
|
|
|
|
2
|
|
|
|
|
|
|
3
|
|
Beds
|
Desks
|
|
|
|
4
|
Number to make:
|
|
|
|
Total Profit:
|
|
5
|
Unit profit:
|
30
|
40
|
|
|
|
6
|
|
|
|
|
|
|
7
|
Constraints:
|
|
|
Used
|
Available
|
|
8
|
Carpentry
|
6
|
4
|
|
36
|
|
9
|
Varnishing
|
4
|
8
|
|
40
|
|
10
|
Desk demand
|
|
1
|
|
8
|
| |
|
|
|
|
|
Which of the following statements represent the carpentry, varnishing and limited demand for desks constraints?
Question 14
The following questions are based on this problem and accompanying Excel windows.
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.
|
Let
|
X1 = Number of Beds to produce
|
|
|
X2 = Number of Desks to produce
|
| |
|
The LP model for the problem is
|
MAX:
|
30 X1 + 40 X2
|
|
Subject to:
|
6 X1 + 4 X2£ 36 (carpentry)
|
|
|
4 X1 + 8 X2£ 40 (varnishing)
|
|
|
X2£ 8 (demand for desks)
|
|
|
X1, X2³ 0
|
| |
|
|
|
A
|
B
|
C
|
D
|
E
|
|
1
|
|
Jones Furniture
|
|
|
|
2
|
|
|
|
|
|
|
3
|
|
Beds
|
Desks
|
|
|
|
4
|
Number to make:
|
|
|
|
Total Profit:
|
|
5
|
Unit profit:
|
30
|
40
|
|
|
|
6
|
|
|
|
|
|
|
7
|
Constraints:
|
|
|
Used
|
Available
|
|
8
|
Carpentry
|
6
|
4
|
|
36
|
|
9
|
Varnishing
|
4
|
8
|
|
40
|
|
10
|
Desk demand
|
|
1
|
|
8
|
| |
|
|
|
|
|
Which of the following statements represent the carpentry, varnishing and limited demand for desks constraints?
Question 15
The constraints X1³ 0 and X2³ 0 are referred to as
Question 16
The following questions are based on this problem and accompanying Excel windows.
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 computers to produce
|
|
|
X2 = Number of Fancy computers 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, X2³ 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
|
| |
|
|
|
|
|
What formula should be entered in cell E5 in the accompanying Excel spreadsheet to compute total profit?
Question 17
The following questions are based on this problem and accompanying Excel windows.
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 computers to produce
|
|
|
X2 = Number of Fancy computers 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, X2³ 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
|
| |
|
|
|
|
|
What formula should be entered in cell D8 in the accompanying Excel spreadsheet to compute the amount of wiring used?
Question 18
Models which are setup in an intuitively appealing, logical layout tend to be the most
Question 19
Which command is equivalent to =SUMPRODUCT(A1:A3,B1:B3)?
Question 20
What does the Excel =SUMPRODUCT(A1:A5,C6;C10) command do?