Microcomputer Manufacturing Optimization Analysis
Budget: $10 – $30 USD
Question 1 (15 points)
A manufacturer of microcomputers produces four models: Portable, Student, Office, and
Network. The profit per unit on each of these four models is $500, $350, $700, and $1000,
respectively. The models require the labor and materials per unit shown below.
Portable Student Office Network Total
Labor (hrs/week) 5 5 6 8 4000
Chassis (unit/week) 1 1 1 1 400
Disk Drive (unit/week) 2 1 2 1 300
Hard Disk (unit/week) 0 0 0 1 20
Memory Chip
(unit/week) 16 8 32 64 22,000
Circuit Bds. (unit/week) 1 1 2 4 10,000
Formulate this product mix problem using linear programming.
Question 2 (15 points)
A manufacturer of microcomputers produces four models: Portable, Student, Office, and
Network. The profit per unit on each of these four models is $500, $350, $700, and $1000,
respectively. The models require the labor and materials per unit shown below.
Portable Student Office Network Total
Labor (hrs/week) 5 5 6 8 4000
Chassis (unit/week) 1 1 1 1 400
Disk Drive (unit/week) 2 1 2 1 300
Hard Disk (unit/week) 0 0 0 1 20
Memory Chip
(unit/week) 16 8 32 64 22,000
Circuit Bds. (unit/week) 1 1 2 4 10,000
How many of each model should be produced to maximize profit. What is the maximum profit?
Question 3 (15 points)
Consider the following linear program:
Maximize 30X + 10Y
Subject to: 3X + Y ≤ 300
X + Y ≤ 200
X ≤ 100
Y ≥ 50
X,Y ≥ 0
(a) Solve the problem graphically. Is there more than one optimal solution? Explain.
(b) Are there any redundant constraints?
Question 4 (15 points)
Billy Penny is trying to determine how many units of two types of lawn mowers to produce each
day. One of these is the Standard model, while the other is the Deluxe model. The profit per unit
on the Standard model is $60, while the profit per unit on the Deluxe model is $40. The Standard
model requires 20 minutes of assembly time, while the Deluxe model requires 35 minutes of
assembly time. The Standard model requires 10 minutes of inspection time, while the Deluxe
model requires 15 minutes of inspection time. The company must fill an order for 6 Deluxe
models. There are 450 minutes of assembly time and 180 minutes of inspection time available
each day. How many units of each product should be manufactured to maximize profits?
Question 5 (15 points)
Given the following data and seasonal index:
Month Sales
Year 1 Year 2
Jan 8 8
Feb 7 9
Mar 5 6
Apr 10 11
May 9 12
June 12 16
July 15 20
Aug 20 25
Sept 4 4
Oct 3 2
Nov 8 7
Dec 9 9
(a) Compute the seasonal index using only year 1 data.
(b) Determine the deseasonalized demand values using year 2 data and year 1's seasonal indices.
Question 6 (10 points)
A large school district is reevaluating its teachers' salaries. They have decided to use regression
analysis to predict mean teacher salaries at each elementary school. The research has come up
with the following prediction equation:
Y = $18012.24 + 1432.37X1 - 4.07 X2 where X1 = Yrs Exp and X2 = Yrs Exp2
(a) If a teacher has 7 years of experience, what is the expected salary?
(b) If teacher has 10 years of experience, what is the expected salary?
Question 7 (15 points)
A large school district is reevaluating its teachers' salaries. They have decided to use regression
analysis to predict mean teacher salaries at each elementary school. The researcher would like to
examine the significance of the following quadratic model for predicting salary based on years of
experience.
Y = β0 + β1X1 + β2X2 + ε where X1 = Yrs Exp and X2 = Yrs Exp2
Salary Yrs Exp
$24,265.00 8
$27,140.00 5
$22,195.00 2
$37,950.00 15
$32,890.00 11
$40,250.00 14
$36,800.00 9
$30,820.00 6
$44,390.00 21
$24,955.00 2
$18,055.00 1
$23,690.00 7
$48,070.00 20
$42,205.00 16
(a) What is the adjusted r2?
(b) What is the prediction equation?
A manufacturer of microcomputers produces four models: Portable, Student, Office, and
Network. The profit per unit on each of these four models is $500, $350, $700, and $1000,
respectively. The models require the labor and materials per unit shown below.
Portable Student Office Network Total
Labor (hrs/week) 5 5 6 8 4000
Chassis (unit/week) 1 1 1 1 400
Disk Drive (unit/week) 2 1 2 1 300
Hard Disk (unit/week) 0 0 0 1 20
Memory Chip
(unit/week) 16 8 32 64 22,000
Circuit Bds. (unit/week) 1 1 2 4 10,000
Formulate this product mix problem using linear programming.
Question 2 (15 points)
A manufacturer of microcomputers produces four models: Portable, Student, Office, and
Network. The profit per unit on each of these four models is $500, $350, $700, and $1000,
respectively. The models require the labor and materials per unit shown below.
Portable Student Office Network Total
Labor (hrs/week) 5 5 6 8 4000
Chassis (unit/week) 1 1 1 1 400
Disk Drive (unit/week) 2 1 2 1 300
Hard Disk (unit/week) 0 0 0 1 20
Memory Chip
(unit/week) 16 8 32 64 22,000
Circuit Bds. (unit/week) 1 1 2 4 10,000
How many of each model should be produced to maximize profit. What is the maximum profit?
Question 3 (15 points)
Consider the following linear program:
Maximize 30X + 10Y
Subject to: 3X + Y ≤ 300
X + Y ≤ 200
X ≤ 100
Y ≥ 50
X,Y ≥ 0
(a) Solve the problem graphically. Is there more than one optimal solution? Explain.
(b) Are there any redundant constraints?
Question 4 (15 points)
Billy Penny is trying to determine how many units of two types of lawn mowers to produce each
day. One of these is the Standard model, while the other is the Deluxe model. The profit per unit
on the Standard model is $60, while the profit per unit on the Deluxe model is $40. The Standard
model requires 20 minutes of assembly time, while the Deluxe model requires 35 minutes of
assembly time. The Standard model requires 10 minutes of inspection time, while the Deluxe
model requires 15 minutes of inspection time. The company must fill an order for 6 Deluxe
models. There are 450 minutes of assembly time and 180 minutes of inspection time available
each day. How many units of each product should be manufactured to maximize profits?
Question 5 (15 points)
Given the following data and seasonal index:
Month Sales
Year 1 Year 2
Jan 8 8
Feb 7 9
Mar 5 6
Apr 10 11
May 9 12
June 12 16
July 15 20
Aug 20 25
Sept 4 4
Oct 3 2
Nov 8 7
Dec 9 9
(a) Compute the seasonal index using only year 1 data.
(b) Determine the deseasonalized demand values using year 2 data and year 1's seasonal indices.
Question 6 (10 points)
A large school district is reevaluating its teachers' salaries. They have decided to use regression
analysis to predict mean teacher salaries at each elementary school. The research has come up
with the following prediction equation:
Y = $18012.24 + 1432.37X1 - 4.07 X2 where X1 = Yrs Exp and X2 = Yrs Exp2
(a) If a teacher has 7 years of experience, what is the expected salary?
(b) If teacher has 10 years of experience, what is the expected salary?
Question 7 (15 points)
A large school district is reevaluating its teachers' salaries. They have decided to use regression
analysis to predict mean teacher salaries at each elementary school. The researcher would like to
examine the significance of the following quadratic model for predicting salary based on years of
experience.
Y = β0 + β1X1 + β2X2 + ε where X1 = Yrs Exp and X2 = Yrs Exp2
Salary Yrs Exp
$24,265.00 8
$27,140.00 5
$22,195.00 2
$37,950.00 15
$32,890.00 11
$40,250.00 14
$36,800.00 9
$30,820.00 6
$44,390.00 21
$24,955.00 2
$18,055.00 1
$23,690.00 7
$48,070.00 20
$42,205.00 16
(a) What is the adjusted r2?
(b) What is the prediction equation?