The City Council proposed to utilize a government-owned land with an area of 15, 000 square meters. One-third of the area will be used to plant mango trees while the rest of the land is where an emergency field hospital shall be built. As the city engineer, you were tasked to determine the following: 1. The dimensions of the land planted with mango trees with minimum cost of fencing given that area is to be rectangular and to be fenced off on three sides not adjacent to the highway.

The City Council proposed to utilize a government-owned land with an area of 15, 000 square meters. One-third of the area will be used to plant mango trees while the rest of the land is where an emergency field hospital shall be built. As the city engineer, you were tasked to determine the following:

1. The dimensions of the land planted with mango trees with minimum cost of fencing given that area is to be rectangular and to be fenced off on three sides not adjacent to the highway.

2. The rate at which the total average of COVID cases is increasing at x = 10 tents and dx/dt = 1 tent per day, given than if 25 tents are built, the average number of COVID cases per tent will be 6 cases while the average number of cases will increase by 2 per tent for each additional tent in the same area due to overcrowding. Verify that values are extrema using either the first derivative test or second derivative test.

As an engineer, cite other instances aside from the situations given above where optimization (one maximization and one minimization) can be applied.