Answered step by step
Verified Expert Solution
Link Copied!

Question

1 Approved Answer

The following questions are based on the problem below and accompanying Analytic Solver Platform sensitivity report. Carlton construction is supplying building materials for a new

The following questions are based on the problem below and accompanying Analytic Solver Platform sensitivity report. Carlton construction is supplying building materials for a new mall construction project in Kansas. Their contract calls for a total of 250,000 tons of material to be delivered over a three-week period. Carlton's supply depot has access to three modes of transportation: a trucking fleet, railway delivery, and air cargo transport. Their contract calls for 120,000 tons delivered by the end of week one, 80% of the total delivered by the end of week two, and the entire amount delivered by the end of week three. Contracts in place with the transportation companies call for at least 45% of the total delivered be delivered by trucking, at least 40% of the total delivered be delivered by railway, and up to 15% of the total delivered be delivered by air cargo. Unfortunately, competing demands limit the availability of each mode of transportation each of the three weeks to the following levels (all in thousands of tons):

Week

Trucking Limits

Railway Limits

Air Cargo Limits

1

45

60

15

2

50

55

10

3

55

45

5

Costs ($ per 1000 tons)

$200

$140

$400

The following is the LP model for this logistics problem.

Let Xij = amount shipped by mode i in week j
where i = 1(Truck), 2(Rail), 3(Air)
and j = 1, 2, 3
Let WLij = weekly limit of mode i in week j (as provided in above table)
MIN: 200(X11 + X12 + X13) + 140(X21 + X22 + X23) + 500(X31 + X32 + X33)
Subject to:
Xij WL ij for all i and j Weekly limits by mode
X11 + X12 + X13 + X21 + X22 + X23 + X31 + X32 + X33 250 Total at end of three weeks
X11 + X21 + X31 + X12 + X22 + X32 200 Total at end of two weeks
X11 + X21 + X31 120 Total at end of first week
X11 + X12 + X13 0.45*250 Truck mix requirement
X21 + X22 + X23 0.40*250 Rail mix requirement
X31 + X32 + X33 0.15*250 Air mix limit
Xij 0 for all i and j

Final

Reduced

Objective

Allowable

Allowable

Cell Name

Value

Cost

Coefficient

Increase

Decrease

$D$6 Week 1 by Truck

45

0

200

360

1E+30

$E$6 Week 1 by Rail

60

0

140

360

1E+30

$F$6 Week 1 by Air

15

0

500

1E+30

360

$D$7 Week 2 by Truck

50

0

200

0

1E+30

$E$7 Week 2 by Rail

55

0

140

0

1E+30

$F$7 Week 2 by Air

0

360

500

1E+30

360

$D$8 Week 3 by Truck

13

0

200

1E+30

0

$E$8 Week 3 by Rail

12

0

140

60

0

$F$8 Week 3 by Air

0

360

500

1E+30

360

Constraints

Final

Shadow

Constraint

Allowable

Allowable

Cell Name

Value

Price

R.H. Side

Increase

Decrease

$D$18 Week 1 by Truck

45

360

45

13

0

$E$18 Week 1 by Rail

60

360

60

15

0

$F$18 Week 1 by Air

15

0

15

1E+30

0

$D$19 Week 2 by Truck

50

0

50

13

25

$E$19 Week 2 by Rail

55

0

55

12

25

$F$19 Week 2 by Air

0

0

10

1E+30

10

$D$20 Week 3 by Truck

13

0

55

1E+30

42

$E$20 Week 3 by Rail

12

0

45

1E+30

33

$F$20 Week 3 by Air

0

0

5

1E+30

5

$D$9 Shipped by Truck

108

60

108

12

13

$E$9 Shipped by Rail

127

0

100

27

1E+30

$F$13 Total Shipped Tons

250

140

250

33

0

$F$9 Shipped by Air

15

0

37.5

1E+30

22.5

$G$6 Week 1 Totals

120

360

120

0

15

$G$7 Week 2 Totals

225

0

200

25

1E+30

$G$8 Week 3 Totals

250

0

250

0

1E+30

The Week 1 by Truck and Week 1 by Rail constraints each have a shadow price of 360. What do these values imply?

Step by Step Solution

There are 3 Steps involved in it

Step: 1

blur-text-image

Get Instant Access to Expert-Tailored Solutions

See step-by-step solutions with expert insights and AI powered tools for academic success

Step: 2

blur-text-image

Step: 3

blur-text-image

Ace Your Homework with AI

Get the answers you need in no time with our AI-driven, step-by-step assistance

Get Started

Recommended Textbook for

The Wall Street Mba

Authors: Reuben Advani

2nd Edition

007178831X, 9780071788311

More Books

Students also viewed these Accounting questions