170 Linear Programming I: Simplex Method
limit on the lengths of the standard rolls, find the cutting pattern that minimizes the trim
losses while satisfying the order above.
3.48 Solve the LP problem stated in Example 1.6 for the following data: l=2 m,
W 1 =3000 N,W 2 =2000 N,W 3 =1000 N, andw 1 =w 2 =w 3 =200 N.
3.49 Find the solution of Problem 1.1 using the simplex method.
3.50 Find the solution of Problem 1.15 using the simplex method.
3.51 Find the solution of Example 3.1 using (a) the graphical method and (b) the simplex
method.
3.52 In the scaffolding system shown in Fig. 3.17, loadsx 1 andx 2 are applied on beams 2 and
3, respectively. RopesAandBcan carry a load ofW 1 =300 lb each; the middle ropes,
CandD, can withstand a load ofW 2 =200 lb each, and ropesEandFare capable
of supporting a loadW 3 =100 lb each. Formulate the problem of finding the loadsx 1
andx 2 and their location parametersx 3 andx 4 to maximize the total load carried by the
system,x 1 +x 2 , by assuming that the beams and ropes are weightless.
3.53 A manufacturer produces three machine parts,A, B, andC. The raw material costs
of partsA, B, andCare $5, $10, and $15 per unit, and the corresponding prices of
the finished parts are $50, $75, and $100 per unit. PartArequires turning and drilling
operations, while partBneeds milling and drilling operations. PartCrequires turning
and milling operations. The number of parts that can be produced on various machines
per day and the daily costs of running the machines are given below:Number of parts that can be produced on
Machine part Turning lathes Drilling machines Milling machines
A 15 15
B 20 30
C 25 10
Cost of running the
machines per day $250 $200 $300Formulate the problem of maximizing the profit.Figure 3.17 Scaffolding system with three beams.