Question

When Ms. Norma Jeane Mortenson decided to run for mayor of Palm Springs, she has identified three issues to capitilize on: traffic congestion (T), garbage collection (G) and flooding during rainstorms (F). Party elders have told her that the number of votes (N) she will get will depend on the hours of time she spends talking about these three issues, namely t, g and f respectively, during her TV commercials, according to the formula: N (t, g, f) = 3 t ^2 + 2 g^2 + f ^2 Since the budget for TV commercials can pay only up to a total 1000 hours and that the total time to talk on issues T and G are not to exceed 400 hours due to political sensitivities, what values of t, g and f will produce the most votes ?

Answer 1

Number of votes Ms. Norma Jeane Mortenson will get is dependent on the hours of time she spends on talking about traffic congestion(t), garbage collection(g) and flooding during rainstroms(f). The function of votes is given below:

N(t,g,f)=3t^2+2g^2+f^2.

Total hours can't exceed 1000 hours. The maximum benefit she gets from taking about traffic congestion. But the total time on T and G can't exceed 400 hours, so she has to talk for 600 hours about flood(f). so, the remaining 400 hours she will talk about traffic congestion and will not talk about garbage collection.

The value of t=400, g=0 and f=600 hours.

The votes are N(400,0,600)=480000+0+360000=840000

if suppose she has chosen t=300, g=100, and f=600 then the votes are N(300,100,600)=270000+0+200000+360000=830000

so, the optimal solution is =400, g=0 and f=600 hours.