The XYZ Company plans to allocate some or all of its monthly advertising budget of $75,000 in the Mankato area. It can purchase local radio spots at $120 per spot, local TV spots at $500 per spot, and local newspaper advertising at $260 per insertion.

The company's policy requirements specify that the company must spend at least $30,000 on TV and allow monthly newspaper expenditures up to $15,000. The companys internal policy also requires that the company must buy at least 100 radio spots.

The payoff from each advertising medium is a function of the size of its audience. The general experience of the firm is that the values of insertions and spots in terms of "audience points" (arbitrary unit), are as given below:

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Radio 150 audience points per spot

TV 180 audience points per spot

Newspapers 280 audience points per insertion

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Let x1 = no. of Radio spots to be purchased,

X2 = no. of TV spots to be purchased, and

X3= no. of Newspaper insertions.

Max 150x1+ 180x2 + 280x3

s.t.

(1) 120x1 + 500x2 + 260x3 <= 75,000 (Advertising Budget)

(2) 500x2 30000 (Expenditure on TV)

(3) 260x3 <= 15000 (Expenditure on Newspaper)

(4) x1 100 (Number of radio spots)

X1, x2, x3 >= 0

LINEAR PROGRAMMING PROBLEM

MAX 150X1+ 180X2 + 280X3

Subject to:

1. 120X1 + 500X2 + 260X3 < 75000
2. 500X2 > 30000
3. 260X3 < 15000
4. 1X1 > 100

OPTIMAL SOLUTION

Objective Function Value = 67050.000

Variable Value Reduced Costs

------------- --------- --------------------

X1 375.000 0.000

X2 60.000 0.000

X3 0.000 45.000

Constraint Slack/Surplus Dual Prices

--------------- ------------------- ---------------

1 0.000 1.250

2 0.000 - 0.89

3 15000.000 0.000

4 275.000 0.000

OBJECTIVE COEFFICIENT RANGES

Variable Lower Limit Current Value Upper Limit

--------------- ------------------ ------------------- ----------------------

X1 129.231 150.000 No Upper Limit

X2 No Lower Limit 180.000 625.000

X3 No Lower Limit 280.000 325.000

RIGHT HAND SIDE RANGES

Variable Lower Limit Current Value Upper Limit

--------------- ------------------ ------------------- ----------------------

1 42000.000 75000.000 No Upper Limit

2 0.000 30000.000 63000.000

3 0.000 15000.000 No Upper Limit

4 No Lower Limit 100.000 375.000

1. Which constraint(s) is/are binding (active)?

2. Interpret the dual price of 1.25 for Constraint 1.

3. The Gold Star Advertising Agency contacted the XYZ regarding the improvement of the effectiveness of the overall advertising campaign. The Gold Star made an offer which guarantees the increase of the total audience points by 5000 points at the cost of $10,000. Should the XYZ accept the offer which requires an increase of the total budget by $10,000? Explain clearly by showing all your work. (10 points)