1. 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.

1.How much of ingredient 3 will be put into the blend?

2.How much resource A will be left unused?

3.What will the profit be?

4.What will happen to the solution if the profit from ingredient 3 increases by 1?

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 Costs

------

X1 0.000 2.000

X2 16.000 0.000

X3 10.000 0.000

Constraint Slack/Surplus Dual Prices

------

1 38.000 0.000

2 2.000 0.000

3 0.000 1.200

4 0.000 -2.600

OBJECTIVECOEFFICIENTRANGES

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

RIGHTHANDSIDERANGES

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

(1) 10 units of ingredient 3 will be put into the blend
(2) 38 units will be left unused
(3) The profit is $166
(4) The profit will increase by $10.

2. An ad campaign for a new resort will be conducted in an area within 2 hours of the resort and can use TV time, radio time, and newspaper ads. Information about each medium is shown below.

Medium / Cost Per Ad / # Reached / Exposure Quality
TV / 600 / 11000 / 35
Radio / 200 / 3000 / 30
Newspaper / 300 / 4000 / 20

If the number of TV ads cannot exceed the number of radio ads by more than 4, and if the advertising budget is $15000, develop the model that will maximize the number reached and achieve an exposure quality of at least 1000. Solve using the Management Science Cd.

  1. Write the objective function for the ad campaign.
  2. In the optimal solution, how many radio ads will be used?
  3. How many potential vacationers will the optimal ad mix reach?

(5) Maximize N = 11000x + 3000y + 4000z,
where x, y and z are the number of TV ads, Radio ads and Newspaper ads respectively
(6) Solution (Using POM-QM):

There will be 16 Radio ads
(7) The ad mix will reach 264500 potential vacationers.

3. Maxwell Manufacturing makes two models of felt tip marking pens. Requirements for each lot of pens are given below.

Fliptop Model / Tiptop Model / Available
Plastic / 3 / 4 / 36
Ink Assembly / 5 / 4 / 40
Molding Time / 5 / 2 / 30

The profit for either model is $1000 per lot. Let F=Fliptop Let T=Tiptop

8. / Write the objective function to maximize profit for Maxwell .
9. / What is the optimal solution?
(8) The objective function is Maximize P = 1000F + 1000T, where F and T are respectively the number of Fliptop and Tiptop models of pens made and sold
(9) Solution (Using POM-QM):

2 Fliptop models and 8 Tiptop models must be made. The profit is $9500.