Chapter 11.2, Problem 1P

Explanation of Solution

a.

Formulating an NLP:

Define the variable as follows,

• $S$ is the number of soap opera ads,
• $F$ is the number of football ads,
• $Z$ is cost function

Non-linear Programming problem to minimize the company’s cost of reaching enough viewers is as follows:

$Min\text{ Z = 50000S + 100000F}$

Such that,

$\begin{array}{l}\text{ x}\end{array}$

Explanation of Solution

b.

NLP violating the Proportionality and Additivity Assumptions:

• Proportionality is referred to as the property by which a change in a variable will result in a proportionate change in that variable’s contribution to the function’s value...

Explanation of Solution

c)

Realistic representation of the number of women viewers:

Consider hypothetically that the number of women reached by $F$ football ads and $S$ soap opera ads is as follows:

$7\sqrt{F}+20\sqrt{S}-0$