Chapter 4.1, Problem 2P

Explanation of Solution

Dorian problem

• Here ${\text{x}}_{\text{1}}$ is the number of 1-minute comedy ads purchased and ${\text{x}}_{\text{2}}$ is the number of 1-minute football ads purchased.
• As there are at least 28 million high-income women, hence the constraint is ${\text{7x}}_{\text{1}}{\text{+ 2x}}_{\text{2}}\text{>= 28}$
• As there are at least 24 million high-income men, hence the constraint is ${\text{2x}}_{\text{1}}{\text{+ 12x}}_{\text{2}}\text{>= 24}$
• Hence the weekly profit is,

  $\text{Z = }\left({\text{27x}}_{\text{1}}{\text{+ 21x}}_{\text{2}}\right)\text{ – }\left({\text{10x}}_{\text{1}}{\text{+ 9x}}_{\text{2}}\right)\text{ – }\left({\text{14x}}_{\text{1}}{\text{+ 10x}}_{\text{2}}\right){\text{ = 3x}}_{\text{1}}{\text{+ 2x}}_{\text{2}}$

• Hence the objective function is,

  ${\text{Minimize Z = 50x}}_{\text{1}}{\text{+ 100x}}_{\text{2}}$

  Subject to