write two satisfactory formulations for this problem: (1) One must include Piecewise Linearization, (2) The other must include all the if conditions mentioned in the lecture Media Selection with Piecewise Linear Functions Dorian Auto has a $20,000 advertising budget.

Dorian can purchase full-page ads in two magazines: Inside Jocks (IJ) and Family Square (FS). An exposure occurs when a person reads a Dorian Auto ad for the first time. The number of exposures generated by each ad in IJ is as follows: ads 1-6, 10,000 exposures; ads 7-10, 3,000 exposures; ads 1115, 2,500 exposures; ads 16+, 0 exposures. For example, 8 ads in IJ would generate 6(10,000) + 2(3,000) 66,000 exposures. The number of exposures generated by each ad in FS is as follows: ads 1-4, 8,000 exposures; ads 5-12, 6,000 exposures; ads 13-15, 2,000 exposures; ads 16+, 0 exposures. Thus, 13 ads in FS would generate 4(8,000) + 8(6,000)+1(2,000) 82,000 exposures. Each full-page ad in either magazine costs $1,000. Assume there is no overlap in the readership of the two magazines. Formulate an IP to maximize the number of exposures that Dorian can obtain with limited advertising funds. = =

(1) One must include Piecewise Linearization, (2) The other must include all the if conditions mentioned in the lecture Media Selection with Piecewise Linear Functions Dorian Auto has a $20,000 advertising budget. Dorian can purchase full-page ads in two magazines: Inside Jocks (IJ) and Family Square (FS). An exposure occurs when a person reads a Dorian Auto ad for the first time. The number of exposures generated by each ad in IJ is as follows: ads 16,10,000 exposures; ads 7-10, 3,000 exposures; ads 11-15, 2,500 exposures; ads 16+,0 exposures. For example, 8 ads in IJ would generate 6(10,000)+2(3,000)=66,000 exposures. The number of exposures generated by each ad in FS is as follows: ads 14,8,000 exposures; ads 5-12, 6,000 exposures; ads 13-15, 2,000 exposures; ads 16+,0 exposures. Thus, 13 ads in FS would generate 4(8,000)+ 8(6,000)+1(2,000)=82,000 exposures. Each full-page ad in either magazine costs $1,000. Assume there is no overlap in the readership of the two magazines. Formulate an IP to maximize the number of exposures that Dorian can obtain with limited advertising funds