LP Model for an Advertisement Example:

Let x1 be the number of comedy spots

Let x2 be the number of football spots

min z = 3000x1 + 7000x2

subject to

120x1 + 30x2 >= 320 (high income women)

40x1 + 90x2 >= 160 (high income men)

x1, x2 >= 0

Useful information (Please do not solve the model, use this information only):

The optimal solution implies that the 1st constraint is nonbinding with an excess value of 16 and the 2nd constraint is binding with a shadow price of 7.5.

Please fill in the blanks below at the story of the given LP model: Dorian makes luxury cars and jeeps for high-income men and women. It wishes to advertise with 1 minute spots in comedy shows and football games. Each comedy spot costs R................. and is seen by .............. high-income women and .............. high-income men. Each football spot costs R................. and is seen by .............. high-income women and .............. high-income men. How can Dorian reach .............. high-income women and .............. high-income men at the least cost?

Please fill in the blanks below at the report (executive summary): The minimum cost of reaching the target audience is R.................. , with .............. comedy spots and .............. football spots.

Find the dual of the LP model given.

What is the allowable range for the objective function coefficient of x2 in which current solution (basis) remains optimal? (Hint: You may use software)

What are the reduced costs for the decisions variables in the model? Why?