The decision variables represent the amounts of ingredients 1, 2, and 3 to put into a blend. The objective function represents profit. The first three constraints measure the usage and availability of resources A, B, and C. The fourth constraint is a minimum requirement for ingredient 3. Use the output to answer these questions. a. How much of ingredient 1 will be put into the blend? b. How much of ingredient 2 will be put into the blend? c. How much of ingredient 3 will be put into the blend? d. How much resource A is used? e. How much resource B will be left unused? f. What will the profit be? g. What will happen to the solution if the profit from ingredient 2 drops to 4? h. What will happen to the solution if the profit from ingredient 3 increases by 1? i. What will happen to the solution if the amount of resource C increases by 2? j. What will happen to the solution if the minimum requirement for ingredient 3 increases to 15? LINEAR PROGRAMMING PROBLEMMAX 4X1+6X2+7X3S.T. 1) 3X1+2X2+5X3<120 2) 1X1+3X2+3X3<80 3) 5X1+5X2+8X3<160 4) +1X3>10 OPTIMAL SOLUTIONObjective Function Value = 166.000 Variable Value Reduced Cost X1 0.000 2.000 X2 16.000 0.000 X3 10.000 0.000 Constraint Slack/Surplus Dual Price 1 38.000 0.000 2 2.000 0.000 3 0.000 1.200 4 0.000 -2.600 OBJECTIVE COEFFICIENT RANGES Variable Lower Limit Current Value Upper Limit X1 No Lower Limit 4.000 6.000 X2 4.375 6.000 No Upper Limit X3 No Lower Limit 7.000 9.600 RIGHT HAND SIDE RANGES Constraint Lower Limit Current Value Upper Limit 1 82.000 120.000 No Upper Limit 2 78.000 80.000 No Upper Limit 3 80.000 160.000 163.333 4 8.889 10.000 20.000

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Description: The decision variables represent the amounts of ingredients 1, 2, and 3 to put into a blend. The objective function represents profit. The first three constraints measure the usage and availability of resources A, B, and C. The fourth constraint is a

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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The decision variables represent the amounts of ingredients 1, 2, and 3 to put into a blend. The objective function represents profit. The first three constraints measure the usage and availability of resources A, B, and C. The fourth constraint is a minimum requirement for ingredient 3. Use the output to answer these questions.

a.	How much of ingredient 1 will be put into the blend?
b.	How much of ingredient 2 will be put into the blend?
c.	How much of ingredient 3 will be put into the blend?
d.	How much resource A is used?
e.	How much resource B will be left unused?
f.	What will the profit be?
g.	What will happen to the solution if the profit from ingredient 2 drops to 4?
h.	What will happen to the solution if the profit from ingredient 3 increases by 1?
i.	What will happen to the solution if the amount of resource C increases by 2?
j.	What will happen to the solution if the minimum requirement for ingredient 3 increases to 15?

LINEAR PROGRAMMING PROBLEM

MAX 4X1+6X2+7X3

S.T.

	1) 3X1+2X2+5X3<120
	2) 1X1+3X2+3X3<80
	3) 5X1+5X2+8X3<160
	4) +1X3>10

OPTIMAL SOLUTION

Objective Function Value = 166.000

Variable	Value	Reduced Cost
X1	0.000	2.000
X2	16.000	0.000
X3	10.000	0.000

Constraint	Slack/Surplus	Dual Price
1	38.000	0.000
2	2.000	0.000
3	0.000	1.200
4	0.000	-2.600

OBJECTIVE COEFFICIENT RANGES

Variable	Lower Limit	Current Value	Upper Limit
X1	No Lower Limit	4.000	6.000
X2	4.375	6.000	No Upper Limit
X3	No Lower Limit	7.000	9.600

RIGHT HAND SIDE RANGES

Constraint	Lower Limit	Current Value	Upper Limit
1	82.000	120.000	No Upper Limit
2	78.000	80.000	No Upper Limit
3	80.000	160.000	163.333
4	8.889	10.000	20.000

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