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 it 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?

### Other samples, services and questions:

When you use PaperHelp, you save one valuable — TIME

You can spend it for more important things than paper writing.