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MGT 455 WEEK 8 CHAPTER B PROBLEM SET

MGT 455 WEEK 8 CHAPTER B PROBLEM SET

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B.1 Solve the following linear programming problem graphically:
 
Maximize profit = 4X + 6Y
Subject to:  X + 2Y <(or equal to) 8
5X + 4Y <(or equal to) 20
X,Y >(or equal to) 0
 
 
 
 
 
B.5
Solve the following LP problem graphically
 
Minimize cost = 24X + 15Y
 
 
Subject to: 7X + 11Y ≥ 77
 
 
 
16X + 4Y ≥ 80
 
 
 
X,Y ≥ 0
 
 
 
B.7 The Attaran Corporation manufactures two electrical
 
 
 
 
 
 
products: portable air conditioners and portable heaters. The
 
 
 
 
 
 
assembly process for each is similar in that both require a certain amount of wiring and drilling. Each air conditioner takes 3 hours
of wiring and 2 hours of drilling. Each heater must go through
 
 
 
 
 
 
2 hours of wiring and 1 hour of drilling. During the next production
 
 
 
 
 
 
period, 240 hours of wiring time are available and up to
 
 
 
 
 
 
 
140 hours of drilling time may be used. Each air conditioner sold
 
 
 
 
 
 
yields a profit of $25. Each heater assembled may be sold for a
 
 
 
 
 
 
$15 profit.
 
 
 
 
 
 
 
 
 
Formulate and solve this LP production-mix situation, and
 
 
 
 
 
 
find the best combination of air conditioners and heaters that
 
 
 
 
 
 
yields the highest profit.
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
B.11 The Sweet Smell Fertilizer Company markets bags
 
 
 
 
 
of manure labeled “not less than 60 lb dry weight.” The packaged
 
 
 
 
manure is a combination of compost and sewage wastes. To
 
 
 
 
 
provide good-quality fertilizer, each bag should contain at least
 
 
 
 
30 lb of compost but no more than 40 lb of sewage. Each pound
 
 
 
 
of compost costs Sweet Smell 5¢ and each pound of sewage costs
 
 
 
 
4¢. Use a graphical LP method to determine the least-cost blend
 
 
 
 
of compost and sewage in each bag.
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Let X be compost and Y be sewage
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Minimize Cost = 5X + 4Y
 
 
 
 
 
 
 
 
subject to
 
 
 
 
 
 
 
 
X + Y ≥ 60
- Constraint A
 
 
 
 
 
 
X ≥ 30
- Constraint B
 
 
 
 
 
 
Y ≤ 40
- Constraint C
 
 
 
 
 
 
X, Y≥ 0
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Determine the feasible region for constraint A. Solve equation X + Y = 60 to determine the feasible region
 
B.21. Par, Inc., produces a standard golf bag and a deluxe
 
 
golf bag on a weekly basis. Each golf bag requires time for cutting
 
and dyeing and time for sewing and finishing, as shown in the following
 
table:
 
 
 
 
 
 
 
 
 
HOURS REQUIRED PER BAG
 
 
 
 
PRODUCT CUTTING AND DYEING SEWING AND FINISHING
 
 
Standard bag 1/2 1
 
 
 
 
Deluxe bag 1 2/3
 
 
 
 
The profits per bag and weekly hours available for cutting and
 
 
dyeing and for sewing and finishing are as follows:
 


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