MAT 540 Week 7 Homework Chapter 3
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1. Southern Sporting Good Company
makes basketballs and footballs. Each product is produced from two resources
rubber and leather. Each basketball produced results in a profit of $11 and
each football earns $15 in profit. The resource requirements for each product
and the total resources available are as follows:
Product
Resource Requirements per Unit
Rubber (lb.)
Leather (ft2)
Basketball
2.8
3.7
Football
1.5
5.2
Total resources
available 600
900
a. Find the optimal solution.
b. What would be the effect on the
optimal solution if the profit for the basketball changed from $11 to $12?
c. What would be the effect on
optimal solution if 400 additional pounds of rubber could be obtained? What
would be the effect if 600 additional square feet of leather could be obtained?
2. A company produces two products,
A and B, which have profits of $9 and $7, respectively. Each unit of product
must be processed on two assembly lines, where the required production times
are as follows:
Product
Resource Requirements per Unit
Line
1
Line 2
A
11
5
B
6
9
Total
Hours
65
40
a. Formulate a linear programming
model to determine the optimal product mix that will maximize profit.
b. What are the sensitivity ranges
for the objective function coefficients?
c. Determine the shadow prices for
additional hours of production time on line 1 and line 2 and indicate whether
the company would prefer additional line 1 or line 2 hours.
3. Formulate and solve the model for
the following problem:
Irwin Textile Mills produces two
types of cotton cloth denim and corduroy. Corduroy is a heavier grade of cotton
cloth and, as such, requires 8 pounds of raw cotton per yard, whereas denim
requires 6 pounds of raw cotton per yard. A yard of corduroy requires 4 hours
of processing time; a yard od denim requires 3.0 hours. Although the demand for
denim is practically unlimited, the maximum demand for corduroy is 510 yards
per month. The manufacturer has 6,500 pounds of cotton and 3,000 hours of
processing time available each month. The manufacturer makes a profit of $2.5
per yards of denim and $3.25 per yard of corduroy. The manufacturer wants to
know how many yards of each type of cloth to produce to maximize profit.
Formulate the model and put into standard form. Solve it
a. How much extra cotton and
processing time are left over at the optimal solution? Is the demand for
corduroy met?
b. If Irwin Mills can obtain
additional cotton or processing time, but not both, which should it select? How
much? Explain your answer.
4. The Bradley family owns 410 acres
of farmland in North Carolina on which they grow corn and tobacco. Each acre of
corn costs $105 to plant, cultivate, and harvest; each acre of tobacco costs $210.
The Bradleys’ have a budget of $52,500 for next year. The government limits the
number of acres of tobacco that can be planted to 100. The profit from each
acre of corn is $300; the profit from each acre of tobacco is $520. The
Bradleys’ want to know how many acres of each crop to plant in order to
maximize their profit.
a. Formulate the linear programming
model for the problem and solve.
b. How many acres of farmland will
not be cultivated at the optimal solution? Do the Bradleys use the entire
100-acre tobacco allotment?
c. The Bradleys’ have an opportunity
to lease some extra land from a neighbor. The neighbor is offering the land to
them for $110 per acre. Should the Bradleys’ lease the land at that price? What
is the maximum price the Bradleys’ should pay their neighbor for the land, and
how much land should they lease at that price?
d. The Bradleys’ are considering
taking out a loan to increase their budget. For each dollar they borrow, how
much additional profit would they make? If they borrowed an additional $1,000,
would the number of acres of corn and tobacco they plant change?
To Get this Tutorial
Copy & Paste above URL Into
Your Browser
Hit Us Email for
Any Inquiry at: Homeworkfy@gmail.com
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More Tutorials: (http://homeworkfy.com/ )
1. Southern Sporting Good Company
makes basketballs and footballs. Each product is produced from two resources
rubber and leather. Each basketball produced results in a profit of $11 and
each football earns $15 in profit. The resource requirements for each product
and the total resources available are as follows:
Product
Resource Requirements per Unit
Rubber (lb.)
Leather (ft2)
Basketball
2.8
3.7
Football
1.5
5.2
Total resources
available 600
900
a. Find the optimal solution.
b. What would be the effect on the
optimal solution if the profit for the basketball changed from $11 to $12?
c. What would be the effect on
optimal solution if 400 additional pounds of rubber could be obtained? What
would be the effect if 600 additional square feet of leather could be obtained?
2. A company produces two products,
A and B, which have profits of $9 and $7, respectively. Each unit of product
must be processed on two assembly lines, where the required production times
are as follows:
Product
Resource Requirements per Unit
Line
1
Line 2
A
11
5
B
6
9
Total
Hours
65
40
a. Formulate a linear programming
model to determine the optimal product mix that will maximize profit.
b. What are the sensitivity ranges
for the objective function coefficients?
c. Determine the shadow prices for
additional hours of production time on line 1 and line 2 and indicate whether
the company would prefer additional line 1 or line 2 hours.
3. Formulate and solve the model for
the following problem:
Irwin Textile Mills produces two
types of cotton cloth denim and corduroy. Corduroy is a heavier grade of cotton
cloth and, as such, requires 8 pounds of raw cotton per yard, whereas denim
requires 6 pounds of raw cotton per yard. A yard of corduroy requires 4 hours
of processing time; a yard od denim requires 3.0 hours. Although the demand for
denim is practically unlimited, the maximum demand for corduroy is 510 yards
per month. The manufacturer has 6,500 pounds of cotton and 3,000 hours of
processing time available each month. The manufacturer makes a profit of $2.5
per yards of denim and $3.25 per yard of corduroy. The manufacturer wants to
know how many yards of each type of cloth to produce to maximize profit.
Formulate the model and put into standard form. Solve it
a. How much extra cotton and
processing time are left over at the optimal solution? Is the demand for
corduroy met?
b. If Irwin Mills can obtain
additional cotton or processing time, but not both, which should it select? How
much? Explain your answer.
4. The Bradley family owns 410 acres
of farmland in North Carolina on which they grow corn and tobacco. Each acre of
corn costs $105 to plant, cultivate, and harvest; each acre of tobacco costs $210.
The Bradleys’ have a budget of $52,500 for next year. The government limits the
number of acres of tobacco that can be planted to 100. The profit from each
acre of corn is $300; the profit from each acre of tobacco is $520. The
Bradleys’ want to know how many acres of each crop to plant in order to
maximize their profit.
a. Formulate the linear programming
model for the problem and solve.
b. How many acres of farmland will
not be cultivated at the optimal solution? Do the Bradleys use the entire
100-acre tobacco allotment?
c. The Bradleys’ have an opportunity
to lease some extra land from a neighbor. The neighbor is offering the land to
them for $110 per acre. Should the Bradleys’ lease the land at that price? What
is the maximum price the Bradleys’ should pay their neighbor for the land, and
how much land should they lease at that price?
d. The Bradleys’ are considering
taking out a loan to increase their budget. For each dollar they borrow, how
much additional profit would they make? If they borrowed an additional $1,000,
would the number of acres of corn and tobacco they plant change?
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