1. Southern Sporting Good
Firm makes basketballs and footballs. Every product is produced
from two assets rubber and leather-based. The useful resource necessities
for every product and the
complete assets out there are as follows:
Useful resource Necessities per Unit
Product Rubber (lb.) Leather-based (ft2)
Basketball three four
Soccer 2 5
500 lb. 800 ft2
a. State the optimum answer.
b. What could be the impact on the optimum answer if the revenue
for a basketball modified from $12 to $13? What could be the impact if the
revenue for a soccer modified from $16 to $15?
c. What could be the impact on the optimum answer if 500
extra kilos of rubber
may very well be obtained? What could be the impact if 500 extra
sq. ft of leather-based
may very well be obtained?
2. An organization produces two merchandise, A and B, which have earnings of
$9 and $7, respectively. Every
unit of product have to be processed on two meeting traces, the place the
required manufacturing instances
are as follows:
Product Line 1 Line2
A 12 four
B four eight
Whole Hours 60 40
a. Formulate a linear programming mannequin to find out the optimum
product combine that can
b. Rework this mannequin into commonplace kind.
three. Resolve drawback 2 utilizing the pc.
a. State the optimum answer.
b. What could be the impact on the optimum answer if the
manufacturing time on line 1 was
lowered to 40 hours?
c. What could be the impact on the optimum answer if the revenue
for product B was elevated from $7 to $15 to $20?
four. For the linear programming mannequin formulated in Drawback 2 and
solved in Drawback three.
a. What are the sensitivity ranges for the target perform
b. Decide the shadow costs for added hours of manufacturing
time on line 1 and line 2 and point out whether or not the corporate would like extra
line 1 or line 2 hours.
5. Formulate and clear up the mannequin for the next drawback:
Irwin Textile Mills produces two sorts of cotton fabric â denim and
corduroy. Corduroy is a heavier grade of cotton fabric and, as such, requires
7.5 kilos of uncooked cotton per yard, whereas denim requires 5 kilos of uncooked
cotton per yard. A yard of corduroy requires three.2 hours of processing time; a
yard of denim requires three.zero hours. Though the demand for denim is virtually
limitless, the utmost demand for corduroy is 510 yards per thirty days. The
producer has 6,500 kilos of cotton and three,000 hours of processing time
out there every month. The producer makes a revenue of $2.25 per yard of
denim and $three.10 per yard of corduroy. The producer needs to know what number of
yards of every sort of material to supply to maximise revenue. Formulate the mannequin
and put it into commonplace kind. Resolve it.
a. How a lot further cotton and processing time are left over on the
optimum answer? Is the demand for corduroy met?
b. What's the impact on the optimum answer if the revenue per
yard of denim is elevated from $2.25 to $three.00? What's the impact if the
revenue per yard of corduroy is elevated from $three.10 to $four.00?
c. What could be the impact on the optimum answer if Irwin Mils
may receive solely 6,000 kilos of cotton per thirty days?
6. Persevering with the mannequin from Drawback 5.
a. If Irwin Mills can receive extra cotton or processing time,
however not each, which ought to it choose? How a lot? Clarify your reply.
b. Establish the sensitivity ranges for the target perform
coefficients and for the constraint amount values. Then clarify the
sensitivity vary for the demand for corduroy.
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